In the end scene with the team celebrating the Day of the Dead, Rossi commemorates a Marine buddy who "we lost in the Tet offensive" which took place in early 1968. In The Fallen (2012), it was established that Rossi's first tour in Vietnam started in 1969.
When the mother hands the unsub the reference book in the library, he takes it with his left hand. But when the shot switches, he has two different books in his left hand and is placing the reference book down with his right hand.
At the crime scene, Reid says of the rocks piled on the body, "These are sedimentary conglomerates with rounded clasts," then goes on, "The rest of this canyon is tertiary rhyolite volcanics, which means the unsub must have brought these rocks with him." - The finder(s) of the body were fossil hunters, they wouldn't be hunting fossils in an area of igneous rocks.
In real life, the scene appears to have been shot in/near Vasquez Rocks, LA County, which are mostly coarse-grained conglomerate and breccia sediments, and are a good place for fossils hunters.
JJ discovers that one of the victims needed corrective lenses to drive, yet she had no glasses or contact lenses on her. When she finds this discrepancy, she says, "Gloria's vision was extremely poor." Drivers' licenses only note that a driver's vision needs correction, not to what degree. Vision only needs correction to 20/40. Vision worse than this still wouldn't be classified as "extremely poor".
The UnSub is said to be descendant of William Stoughton--however, Stoughton was a bachelor with no children, therefore he has no direct descendants.
The unsub is stacking rocks at the beginning and they are quite obviously not real as he moves them with ease.
In the prologue, Reid impersonates Clint Eastwood in the title role in Dirty Harry (1971) by saying "I know what you're thinking: 'Did that guy fire six shots, or did he fire five shots?...'" The actual quote is "I know what you're thinking: 'Did he fire six shots, or only five?...'" Between Reid's eidetic memory and the fact that this is one of the most repeated movie quotes of all time and said twice in the movie, his quote should have been much more exact.
The librarian chastises the unsub for refusing to check out a reference book, saying "this is a lending library." Most lending libraries also have a selection of reference books that cannot be checked out. If the book was a reference book, he was correct in not allowing it to be checked out and suggesting photocopying the book.
The librarian says that she "logged" the book in. This is not terminology used by librarians. She may mean that she catalogued the book in order to add it into their integrated library system. However, it would be strange for a book to be in a public part of the library and for it not to have already been catalogued because cataloguing is done when a book is first received before putting it on a shelf. Seeing that the book had never been catalogued would indicate to the librarian that the book may not belong to the library.
Reid states "witches were thrown off cliffs, hung, slowly crushed by rocks". As educated as he is, he should know objects are hung, people are hanged.