View of the Hebrews
A man named Ethan Smith published a book in 1823 called "View of the Hebrews," which outlined many parallels between American Indians and Hebrews. Some of these parallels are also found in the Book of Mormon. So, some people think that Joseph Smith got those ideas from Ethan Smith's book.
The most obvious problem with this line of attack against Joseph Smith is that the people who make it are willing to claim on the one hand that the parallels between View of the Hebrews and the Book of Mormon are a sure sign of a connection between the two, yet they outright dismiss the notion that the many parallels listed between Hebrews and American Indians could be a sign of a connection between them, calling those parallels mere coincidence.
Parallels are tricky, because there aren't all that many "different" themes to talk about in an ancient Judeo-Christian context, and the Book of Mormon covers just about all of them. So, we shouldn't be surprised to find parallels between the topics covered in the Book of Mormon and the topics that would be found in any book that addresses the idea of Hebrews coming to America in ancient times. Much more significant are the parallels found between the much shorter Book of Abraham, which covers far fewer themes, and the content of ancient documents such as the "Apocalypse of Abraham." These records share many common - and unexpected - themes in a relatively small number of words. So if one believes the View of the Hebrews constitutes overwhelming evidence that Joseph Smith derived ideas for the Book of Mormon from another source, but dismisses the evidence that the Book of Abraham and ancient stories about Abraham ultimately stem from a common source, then I'd like to know why they are so convinced in the one case and so dismissive in the other.
Like the Book of Abraham connection to Abraham stories, I believe the Book of Mormon is indeed connected in some way with View of the Hebrews, in that they both derive from the fact that Hebrews came to ancient America. Ethan Smith may have gone overboard in some of his parallels between Hebrews and American Indians, but I do find many of the parallels interesting. Ethan Smith could very well have been inspired to write his book in order to prepare some people to accept the Book of Mormon.
Lack of Evidence of Hebrew Culture
Unlike Ethan Smith, many people see a lack of evidence of Hebrew culture in pre-Columbian America. However, this is not unexpected. Enos tells us that the Lamanites would, if possible, "destroy our records and us, and also all the traditions of our fathers" (Enos 1:14). In other words, they would destroy any traces of Hebrew culture. That's what Hitler tried to do. The difference is, the Lamanites succeeded, or nearly succeeded (Moroni 1:1-4). Furthermore, we don't know very much about Ancient Hebrew culture prior to the destruction of Jerusalem. In fact, most of the Ancient Hebrew language and grammar have been lost, and the only document for us to analyze is what has been preserved in the Old Testament. Everything changed after the destruction of Jerusalem.
Moreover, we need not suppose that Lehi and his followers attempted to transplant their entire culture here. More likely, they adopted the ways of the native population which was already here, with regard to most things.