"The Book of Solomon" is supposed to be 3,000 years old, but is shown as a modern book. Bound "books" (codices) were first created by the Romans in the 1st century AD. Leather covered, bound books such as that shown did not come into existence until the 15th century in Europe.
When Flynn first sees the map, he says it has strange characters on it, when they are, in fact, hieroglyphics. Since he's got at least one degree in Ancient Egyptology (according to the first movie), shouldn't he have recognized the characters for what they were?
In the beginning the man being chased through the streets stands against a red wall. Before he does you see the back of his shirt covered in red. In the shot after he stands against the wall his shirt is clean.
In the first movie, Quest for the Spear, Flynn is stated as having been in college for 16 years. In the beginning of this, the second movie, Return to King Solomon's Mines, he has his 32nd birthday and has worked over a year as the Librarian. Even if Flynn started college at the age of 17 he would have only been able to squeeze in 13 years of college when he became the Librarian at age 30.
In the first scene of "The Librarian - Quest for the Spear" (at the recreation of the pyramid), Flynn states that he has 22 degrees; his professor states that the degree he was currently working on was signed off. This now makes a total of 23 degrees. Flynn states at least twice in "Return to King Solomon's Mines" that he has 22 degrees. In addition, Emily states early in the film that she has 25 degrees and is beginning work on her 26th in June; at the end of the film, Flynn says that she has 25 PhDs.
The scroll leading to King Solomon's mines is supposedly 3000+ years old, however Carson uses modern music notes and a five line staff to interpret it. The five line staff and modern music notes (like those shown on the scroll) weren't used until the early Baroque music period (mid 1600s).
Early in the film, Emily mentions Solomon as having reigned in the 10th century BC. A little later she refers to features of landscape as having been looked at by Solomon and/or the queen of Sheeba TWO thousand years ago.
Although they got the name of the common Vampire Bat correct, the bat that is shown in the movie cannot be any species of vampire bat. As there are only 3 species of Vampire Bats all of which are found only in South America and Mexico. Also none of them have red eyes or are that big. Vampire Bats are very small.
When Flynn and Emily are in Solomon's treasure chamber, Flynn holds up a scroll and calls it the Dead Sea Scrolls. The Dead Sea Scrolls are so named because they were found along the Dead Sea in caves in the 1940's. They were written and stored there by a community of Jews who lived around the Dead Sea just a few hundred years before the birth of Jesus, many centuries after Solomon was alive.
When Flynn and Emily are in Solomon's treasure chamber, Emily holds up a book that she recognizes as Genesis. However, it is bound like a modern day book, which didn't happen for many centuries after Solomon lived.
If all Flynn has to do is prevent the Key of Solomon falling in to the wrong hands, he would only have to return to the library with the part of the key he found at the dig in Casablanca to accomplish this. However, Judson tells him he is done, and tells him to return but he disobeys.