Aside from every sort of problem involving the Rosetta stone and the clear fact that at least one of the "holy books" of the LDS church is a proven fraud, there is the question of archaeology. The bom posits an Israelite or Israelite-related civilization transplanted into the Americas in biblical times and there would have to be archaeological evidence of that as well as traces of that in the dress, names, languages, customs etc. of the American natives who the Spanish found around 1500 AD, and as far as I know, there isn't any. A civilization like that could not plausibly vanish without a trace.
If you factor in recent research into med-basin chronologies the problem gets even worse. The best experts on those topics, i.e. people like Gunnar Heinsohn, Charles Ginenthal, and Emmet Sweeney, are now claiming that there truly isn't any med-basin history any older than about 3000 years starting from now.