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, in the Darth Vader cameo, a LucasFilm employee came on-set to observe the scene and tell the filmmakers what Vader would or wouldn't do.
The first movie filmed in the Smithsonian Institution.
(at around 41 mins) When first introduced to Napoleon Bonaparte and Al Capone, Ivan the Terrible says his title is mistranslated, and he calls himself "Ivan the Awesome". This is basically true: Ivan's title is indeed a bad translation. His Russian name is Ivan Grozny, and the word "grozny" does not have a bad connotation. A more accurate translation might be "Ivan the Fearsome", "the Magnificent", or "The Admirable".
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 a Boris Karloff impersonation.
One historical detail not mentioned in the film is that many of the taxidermy specimens on display in the Smithsonian's Natural History Museum were shot by Teddy Roosevelt himself on his safari trip in 1913, including the lion standing on a pedestal in the Hall of Mammals.
Clint Howard: (at around 1h 4 mins) Ron Howard's brother appears as a flight commander in the Aeuronautic Center. He did the same role in Apollo 13 (1995), directed by his brother.
Thomas Lennon, Robert Ben Garant: (at around 1h 10 mins) The Screenwriters play Wilbur Wright and Orville Wright.