Director Shawn Levy told a National Public Radio interviewer that once the Smithsonian Institution agreed to lend their name to the film, their curators were very helpful and willing to share information about the real-life characters represented in the movie, but Levy had more trouble with the intellectual property-holders for the fictional characters represented. For instance, for a scene in which Darth Vader interacts with the pharaoh played by Hank Azaria, there was a person on the set who came from LucasFilm and whose job it was to observe all scenes filmed that involved Darth Vader and to tell the filmmakers what Vader would or wouldn't do.
The motorcycle that Larry uses as a getaway vehicle is a rare 1942 Harley Davidson XA Military Side Valve 750cc Flat Twin with attached sidecar. This was Harley's copy of the German BMW/Zundapp military motorcycles.
Amelia says in the movie that she became a pilot, "for the fun of it!" This refers to the book Amelia Earhart wrote called 'The Fun of It' (1932). It is a memoir of her flying experiences and an essay on women in aviation.
The Smithsonian does host a giant squid exhibit, but this was forgone for a giant octopus in the film. For some reason, however, the film's marketing in Japan (where the difference between a squid and an octopus is common knowledge) consistently referred to the octopus as a "squid," even though it is never directly identified as either animal in the film.
Hank Azaria filmed test scenes (some of which are on the DVD) of his character Kahmunrah with various accents including American Southerner (from Alabama) and English Cockney, before settling on an upper-class British accent marred by a humorous lisp.
The trivia item below may give away important plot points.
Near the end of the movie, Larry and Jed notice that Amelia Earhart has flown off in the wrong direction. Later, when Larry meets the human lookalike, she asks for help getting to the miniature room because she gets lost. This is a reference to Earhart's last known flight where she disappeared, not having any idea where she and her navigator were at.