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.
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 guy who gets his car stolen by Ed Harris in London is the same guy who got his car stolen by Sean Connery in The Rock, another of Jerry Bruckheimer's movies which also starred Nicholas Cage and Ed Harris.
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.
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.
According to the website Ten Facts About the Mansion-Mount Vernon, Mount Vernon has a full basement, but there are no secret passages leading from it. The Mansion basement or cellar played a key role in the movie National Treasure: Book of Secrets and although there is no tunnel leading from it, it was an extremely important part of life in the Mansion. The cellar was used for a variety of purposes and was divided into several rooms. One room, closest to the kitchen, has a large fireplace and was used as a dining area for the housekeeper and other white servants as well as to heat food before it was served to the Washington's. When Washington died in 1799 there were a variety of items stored in the basement including wine, sand for rustication, and potatoes.
When Ben and Abigail visit the White House, Ben gets into a confrontation with a small boy. When the boy goes to leave he can be seen curling the index finger on his left hand. In another Disney movie The Kid with Bruce Willis this finger curl is a trait of the young Russ Duritz played by Spencer Breslin. This movie was also directed by Jon Turteltaub, the finger curl is a sign of annoyance.
The Ferrari which gets impounded in the first minutes of the film is a Ferrari F430 Spider. However at the end of the film he is seen in a different car, the Ferrari 360 Spider, which is the same model he drives at the end of the first movie.
The trivia items below may give away important plot points.
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.
It shouldn't 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.