In the first edition of the Book of Mormon, in Mosiah 21:28 (continuing from Mosiah 8:13-14) Ammon tells Limhi that King Benjamin has the ability to translate the ancient records his people found. Problem is, Benjamin was not the king at this point in Nephite history. It was actually his son Mosiah. Joseph Smith realized this mistake, and changed it to Mosiah in the 1837 edition.

A similar problem can be found in Ether 4:1 where the first edition of the Book of Mormon stated King Benjamin kept certain things from the Jaredite record secret, when it was actually his son Mosiah that translated the Jaredite plates. (Mosiah 28:10-19) The Church realized this problem after joseph Smith’s death, and changed Benjamin to Mosiah in the 1849 edition.

The next internal chronology error is the discrepancy on the year Helaman departed with his 2000 Lamanite warriors. According to Alma 53, this occurred in the 28th year of the reign of the judges, whereas in Alma 56, it takes place in the 26th year. Viewing the two chronologies side by side, they are completely irreconcilable, so the Church was not able to correct this problem, and it still stands in our current editions.

The greatest number of discrepancies that occur in the Book of Mormon, however, concern it quoting Bible passages decades or centuries before they were written. This problem is so widespread that it would be impossible to cover it one post, but here are a few examples:
1 Nephi 22:15, 23-24; 2 Nephi 25:13 quote Malachi 4:1-2. However, according to the Book of Mormon chronology, Nephi lived 200 years prior to Malachi.

In 2 Nephi 2:5 Lehi quotes the apostle Paul in Romans 3:20. But Lehi supposedly lived 600 years before Paul.

Alma 7:24 is a combination of 1 Corinthians 13:13 and 2 Corinthians 9:8, but Alma supposedly lived more than a century before these epistles were written.

Helaman 5:8, 12 has two clear references to the Sermon on the Mount, but this was allegedly written in 30 BC, more than 60 years before the Sermon on the Mount existed.