1) metal (coins, swords, armor) do not disappear. There are multiple museums and storage rooms full of contemporarily-same Persian, Asian, European, African metal artifacts from the same period. Metallurgy simply changes societies, and no pre-Columbian metal artifacts of antiquity are found in the Americas
2) Meso-American (Aztec, Olmec) cultures were not Judaic or Christian. North American cultures (Hopewell, etc.) the same. Look at the surviving architecture. No non-LDS archeologist supports the idea of a Judeo-Christian Olmec, Aztec, Hopewell, or Incan culture anywhere in the Americas, and similarly the Smithsonian, our nations leading scientific (oops, 4-letter word :) institution, has made written statements as to this. The church has smartly backed away from BOM archeological claims in its Gospel Topics Essay. In Nov, 2021 Pres Nelson rightly said, "The BOM should not be read as a historical document, but as a spiritual document." So, time to hang up on the historicity claims (that's good).
3) there are no mega structures cities and surviving stone walls in North America, and major walls and cities across an entire area don't just disappear (Pompay was under volcanic ash and has been excavated, old Alexandria slipped into the sea and one can scuba dive and see those walls, Hadrian's Wall in contemporary England and many Roman walls still exist, the Wall of China still exists, etc.). Stone and cement walls do not disappear.
4) elephants, pre-Columbian horses, oxen: bones do not just disappear (we still have dinosaur bones, despite the catastrophic event that took them out)
5) DNA evidence does not support (DNA tests clearly show Native American people of Asiatic, not Middle Eastern, origin). The church modified the BOM title page from American Indians being "direct descendants of Lamanites" to "among the descendants" (as DNA testing shows Asiatic origin, not middle eastern or near eastern), and the church published a Gospel Topics Essay on this in the early 10's, and now they simply say the origins may never be known.
6) Linguistic authorship does not support:
a) many analyses now show similarities to contemporary books and newspapers of the time
b) entire verses (not to mention Isaiah) are replicas of KJV, both OT and NT
c) Apologists make the BOM out to be more than it is linguistically and literarily (e.g. the poem Hickory Dickory Dock is a poetic chiasmus)
d) if an 1829 book used Hebraic words (names, cities), it doesn't make it of Reformed Egyptian origin. We can use Hebraic words now in current text. because Joseph Smith used Hebrew words in the BOM, does it make the book of ancient origin?
e) and lastly to consider, many of the names and cities in the BOM have strong resemblance to other cities, areas, countries that were known to Joseph's time (Cumoras Islands, Lehigh Valley in PA, Moroni, etc.).
7) anachronism: when the KJV scholars did their translation in 1620 they added italics for added or non-matching words. The BOM manuscript (and current editions still) have those exact italics (JS or OC copied the 1620 KJV exactly). Did ancient Jewish authors/rabbis write Isaiah on the Plates of Brass thousands of years ago with the italics that the King's scholars added in 1620, or did Joseph copy the 1620s KJV of Isaiah word for word, including the italicized words those scholars had added?
8) many sources of contemporary books and newspapers were available to JS, and many similarities exist:
a) View of Hebrews, Spaulding Manuscript (the original, not the revised), the KJV Bible (replicated stories and verses, Isaiah was copied directly from 1620s KJV, italics as all), Emanuel Swedenborg's "Heaven and Hell," Thomas Dick's "Future State," The Healing of Nations, The First Book of Napolean, The Chronicles of Eri, the Book of Nullification, The Late Great War, etc.) Joseph was literate (taught by Alvin, who attended Dartmouth) and he was a genius.
b) a good amount of LDS doctrine is already found in these contemporary 1700s/early 1800s books (pre-existence, Native Americans as House of Israel, a former white race killed off by the Native Americans, three degrees of glory, etc.). These were topics being commonly speculated upon and were written about even by the Governor of NY and various newspapers of Joseph's time.
c) similarly, a lot of LDS doctrine is not novel. Recall that SR was a professional minister in Cleveland of the American Restoration Movement, aka Stone-Campbell movement (present day Church of Christ and Disciples of Christ. You can see Stone-Campbell doctrines (restored priesthood, etc.) in LDS doctrine. It was JS and OC in BOM 1829 publishing time (Oliver was from the same town as View of Hebrews author and attended his congregation), but by 1835 JS was well established in Kirtland with really advanced theologians such as Sydney Rigdon, and that's when the first bulk of "modern" doctrine came about (second period being Nauvoo, which is where Joseph started preaching privately about Theocratic Kingdom of God on Earth, polygamy, becoming a God, etc.). Joseph's stretching stuff was in the Nauvoo period. The Kirtland period was a beautiful amalgamation of collected and composed material. I do believe Joseph heavily borrowed from ideas and content of the time, but I also believe he was inspired. Sadly, he got derailed though morally.
9) gold plates: very apologetic and interesting claim to say God took them off the earth to increase our faith (Occam's Razor is a better place to start!)
10) speaking of plates, research Kinderhook plates, a hoax set for JS by local farmers which he fell for (they created plates and gave them to him to translate, he attributed them to be of Jaredite timeframe and a T and S article was published showing a drawing of them and saying that Joseph would have them translated and available for sale by Spring). The LDS church has those Kinderhook plates in their possession; they had them on display until the early 1980s (I saw them in the museum west of the tabernacle), and they stopped displaying them when scientific analysis showed them to be (as the farmer's who created and laid them claimed) of 1800s origin. That same museum used to display Indian relics as well, suggesting that all American Indians and Aztec/Olmecs and Polynesians were of "Lamanite" origin. The Church has a good Gospel Topics Essay on Race, and they now no longer make that claim. I respect the church for their essays -- and they don't promote them in Sunday reading, so the myths live on and people can be defensive, until they hear or read what the church says -- and then turn on a dime from that external direction.
11) the witnesses were unreliable:
a) the witnesses were either Smiths (dad, brothers), Whitmers (or relatives of like Oliver Cowdery, who married in), or Martin Harris. Relationship of the witness to the person is key to credibility in any investigation or proceeding and is a sound measure of evidence.
b) many were unreliable characters, e.g. read what BY and JS aid about Martin Harris. Harris joined five churches before Mormonism, his wife said he was trying to profit from it, he said he saw God as a deer in the forest, he said he had a Godly creature on his chest whom only he could see, and like most of the other witnesses he later witnessed to the ancient authenticity of the Voree plates of James Strang, who led a group of disaffected Mormons to MI, after the schism in Nauvoo 1844.
c) many of the BOM plates witnesses went on to be signed witnesses for plates "found" (created) by James Strang, which he called the "Voree" plates. Strang was a man who claimed he had a letter from JS to make him the successor (he, Sydney and Brigham were the men there on 8/8/1844 vying to be the successor). Many people followed him to MI (an island in Lake MI), and many of the same BOM witnesses signed the same-type of worded witness statement of the Voree plates, that they appeared to be of ancient origin with ancient characters, etc. Those plates survive and are scientifically shown to be of 19th century origin. Credibility of witnesses is key in establishing truth.
d) all witnesses later indicated they "saw and felt" the plates with their "spiritual eyes" (in a vision), and Matin Harris gave a very specific account that he was having difficulty picturing them and so Joseph had to take him outside, into the woods away, and help him to pray so he could see with his spiritual eyes. the "hefting" were metallic plates under a towel, and once in a wooden box. The "feeling of the plates" (Emma, while the plates were on the kitchen table) was under a towel. It's very likely that Joseph had plates (metallic plates would be easy to create).
3) all the witnesses either left the church or were excommunicated. David Whitmer in 1838, like Oliver Cowdery, had stated concerns about Joseph's morality (alleged affair with Fanny Alger, which the LDS church now claims was his first wife). Whitmer was also stated concerns about Joseph's late introduction of the first vision story, of its changing nature, and of changing doctrine. I think many people in Kirtland were disillusioned by what they likely perceived as Joseph's greed with the banking scandal. Whitmer was excommunicated for failure to observe the word of wisdom (laughable for its time, JS had a bar in his Nauvoo Mansion home), and for speaking ill of the Lord's anointed (for stating concern about Joseph's affair with Fanny).
4) Joseph tried to profit from the BOM, D and C records how he sent men (three) to Toronto to sell the copyright of the book (all printing rights would be given up). When the Nauvoo House cornerstone was laid Joseph placed the original manuscript (!) into the cornerstone as a time capsule (sadly, poorly sealed and badly water damaged when later recovered). Joseph was asked why and he is recorded as saying "That book has caused me enough trouble."
5) if is the most perfect book ever made, if it can get a person closer to God than any other book, why the issues, and why the changes: granted, mostly grammatical, but there have been significant content changes such as "white and delightsome" changed to "fair and delightsome," etc.
6) Moroni 10 gives a nice pattern and challenge to read the book, ponder and pray about it.
a) reading and pondering is what investigators and members are asked to do, but once you're a member you are only supposed to read from church-approved materials. is that a good method?
b) having a feeling about a book is something that can be good, but you can't pin your entire testimony of the church on it. The LDS pattern is kind of carte blanche, that you get a warm feeling and then you know it is all true. People and histories are nuanced, anything touched by man is not all true. Joseph made claims of the BOM's historicity (and the BoA), it's clearly shown to not be a historical document (as President Nelson said last Nov) -- so by the church's own measure it Is or Is Not, and therefore Joseph Smith Was or Was Not. It's that kind of absolutist approach that gets the church in trouble with itself.
7) further on evidence, the BOM talks about final battles (Jaredite) with millions of people at the Hill Cumorah. Such a battle would have been bigger than any recorded in Asian, African, or European history. And no artifacts. The surrounding areas of the hill have had ground penetrating radar, metal detection -- and it's declared "a clean and unremarkable site archeologically." Millions of bones, swords, armor would be there. And similarly, no such finds anywhere in the Americas (b/c there was no metallurgy here, dang striaght you'd have artifacts if there were, metal changes societies). Joseph's math and story of huge battles wasn't just grandiose in contrast say to Greek, Roman or Persian numbers and conquests, but it makes archeology that much more findable at that large scale. The lack of bones and metal, show that those claims of large battles in the BOM are not factual. Again, RMN declared it a "spiritual document' (not a "historical document" last year -- b/c he had to! It's time to give up the sacred story tied to history. Things can be non-historical and simply a valuable story to learn from. But let's not fool ourselves by promoting non-true statements of our myths and sacred stories as historical facts.
The LDS Church Gospel Topic Essay on BOM acknowledges a lot of these issues; I highly recommend all LDS members read those essays (they're hard to find on the church website, yo have to use the search tool). They're where I started. What you'll find in those church essays is that many things that are considered anti-Mormon, things which authors had been excommunicated for, are acknowledged by the church.
Mark Twain said he wouldn't be convinced of gold plates if the whole rest of the Whitmer family had seen them! And he criticized the literary construction and prose (the over-use of "And it came to pass and the use of 1620s, non-colloquial even for its time, wording -- so it would sound more scriptural). The BOM reads like a modern document, b/c it is. There's a reason OT reads so foreign to us and God can seem like an angry desert God (b/c that was their justice God of the time).
Lucy Mack Smith noted in her auto-biography (early 1850s) that Joseph was a highly imaginative boy and as a youth (before the plates), that he'd tell fantastical stories of the Indians, how they lived, what their modes of transportation were and what food they ate (BTW the BOM does not mention corn but does mention wheat -- corn would have been a staple of Meso-American and North American diet, while wheat was introduced to this continent by the Spaniards and Portuguese).
Scripture is limited by the world views of the author (e.g. Paul said women should stay silent in church), and OT customs 4-5k years ago were vastly different (Leviticus says someone who works on Sunday should be killed, that a man who rapes a woman should pay her father, etc.). The OT was so long ago that it seems like an angry desert God of justice, as those were the times and ways.
The BOM reads more modernly, as it was written in 1829 (although the prose of 1620s KJV was used to enhance is scripture sheek!), b/c that was the author's (JS) timeframe.
In the end, what is scripture? Does it have to be historical to be true, or should we simply gain the good from the meaning we discern from the story? Yes BOM is problematic for the above reasons, and for the fact that JS claimed it was ancient and from gold plates now in heaven - but the book is an incredible work and it does testify of Christ and speaks to social issues of Joseph's time, e.g.
a) answering for his view, the question about the American Indians
b) cautioning on the danger of secret societies (which ironically JS later joined and promoted)
c) setting a utopian society for hundreds of years when there were no matter of 'ites
In the end, scripture does not have to be be historical, so regardless of BOM's ancient historicity or not, if the book helps you be a better person and it's good for you, then it's good for you! I appreciate the BOM for that and it guided me well for many years
Aside from the parts copied from his version of the bible, the book was written by scribes as dictated by Joseph Smith. He was known as a particularly good orator and often gave sermons for hours without any prepared notes. He also practiced telling stories about native Americans as a teen based on legends of the mound-builders of Hebrew heritage which, per his mother, entertained his family for hours. He borrowed stories like Lehi's vision of the tree of life from his father's experience and contemporary religious themes (like baptism of infants) from local preaching. His deep immersion in a biblical/ magical christian community may have been a source for some hebraisms (such as names and chiasmus) as they continue to appear in subsequent revelations.