Peter Bartley lists Deutero-Isaiah, use of 1 Corinthians 12-13, and Synagogues as being anachronisms in the Book of Mormon.
Peter Bartley, Mormonism: The Prophet, the Book and the Cult (Dublin: Veritas, 1989), 62
Joseph Smith committed another faux pas when he included Isaiah 48-51 and 53 in the Book of Mormon. The Nephite prophets could not have possessed these texts. It is now a widely-held view of scripture scholars that Isaiah was the work of at least three authors, and that the eighth century Isaiah was responsible for chapters 1-39 only. Chapters 40-55 known as Second or Deutero-Isaiah, was the work of an unknown prophet living in Babylon towards the end of the Exile. Since the Exile lasted from 587 to 538 BC, and the Nephites left Jerusalem in 600 BC, they could not have taken with them ay part of the Book of Isaiah beyond chapter 39, as the rest of the book had not yet been written.
While certain aberrations in the Book of Mormon have come to light as a result of a better understanding of the Bible, others simply defy common sense. One wonders how it was possible for a Book of Mormon scribe to have been so familiar with the teaching of St Paul to include in his own passages from 1 Corinthians 12-13. And how could the prophet, Ether, have told the ancient Jaredites of the New Jerusalem to be erected in the land of America, when he and they knew nothing of the Old Jerusalem? Also, one marvels at how an institution such as the synagogue could have emerged independently as a fact of Jewish life in both the Old World and the New. Synagogues were known at the time the Nephites left Jerusalem. These are but a few examples; many more could be cited.