The area of the Library of Congress that Gates finds the Book of Secrets in does not exist as an area of book shelves. These book shelves were constructed as a prop library in a previously empty balcony of the Library's Main Reading Room and dismantled after the scenes were shot.
When showing the map of the grounds to the President, Ben tells him it belonged to a slave of Washington's named Charlotte. This is the same name as in the clue to the Templar treasure that Charles Carroll gave to Gates' ancestor (and which turned out to be the name of a ship). Presumably Mt. Vernon was one of many dead ends which Ben pursued in his search for Charlotte and the Templar treasure prior to the events of the first movie, which would explain why he knew about the hidden compartment and how it worked, or it might just be a sly reference to the first National Treasure (2004).
The night before the scenes at the University of Maryland were to be filmed a half inch of snow fell. The crew then had to use fire hoses to hose down the entire McKeldin Mall and nearby locations to melt the snow for continuity in the movie.
In the Booth diary the remaining part of the page after the words Thomas Gates Artifex (artifex: Latin) adj., skilled, masterful) is the word Aenigmatum, or enigma. The Latin word and Greek word brought together mean one who is skilled in puzzles.
It should come as little surprise that Patrick Gates would be associated with the Confederacy. In the original National Treasure (2004), Patrick Gates displayed in his library a portrait of CSA General Thomas "Stonewall" Jackson.
The script originally called for Mitch Wilkinson to stab Patrick Gates in the scene where they escape from the flooding gold city. This was taken out in post because it made the character "cross a line" that the director felt ought not be crossed. This is why there are almost no shots of Patrick Gates remaining in this scene: he was bleeding, and that's hard to hide. His sweater in the next scene had been ripped from the stabbing, and they were able to "unrip" his shirt with CG.