Some critics, particularly Evangelical Christian critics, have pointed out in the past that it is inconceivable that the Nephites could have built temples in the New World because “real Jews” would never do that in violation of their law.
As an example, consider the following from a page published by the Institute for Religious Research. (I’ve take the liberty of removing the scriptural references from this excerpt.)
The people described in the Book of Mormon operated multiple temples. This violates the dictates of the Old Testament Scriptures on two counts: First, God commanded Israel to build only one temple to reflect that fact that there is only one true God. Second, the one legitimate temple was to be built in Jerusalem (Zion), the location designated by God.
The folks are IRR aren’t alone, however. Similar criticisms have been made by James White (Alpha and Omega Ministries). Bill McKeever (Mormonism Research Ministry), in telling people how to prepare for a tour of the temple, that “the Jews recognized only the Jerusalem temple as being God-ordained.” Living Hope Ministries, in their video The Bible vs. The Book of Mormon, focuses on how Jews would never think of building a temple outside of Jerusalem.
Such an argument, however, demonstrates nothing but a lack of knowledge concerning the actual practices of ancient Jews. The fact is that ancient Jews did build temples outside of Jerusalem, and they built a lot of them. The Nephites were exiles from ancient Israelite culture, and would have continued the practices of temple building and worship that they were familiar with.
More detailed information concerning temples in the Book of Mormon can be found at the FAIR wiki. The following video, recently put together by Tyler Livingston, will also be informative on this subject.