When Adelina and her servant Ricardo confront Lionel and Mr. Link for breaking in, Ricardo accidentally fires his blunderbuss at the safe, which not only blows a hole into it, but sends it flying a good 15 to 20 feet back. Real-life blunderbusses are nowhere near this powerful, and even if it were, it would have an insane amount of recoil that would send Ricardo flying backwards.
Though the film takes place no later than 1886 (as evidence of the Statue of Liberty being shown under construction), Mr. Link has zips up his pants, decades before the zipper was patented.
A map of the United States is shown in the film. It shows several states which weren't yet states as of the film's 1886 setting (for example, Arizona didn't become a state until 1912).
Washington is referred to as a state but the film is set in 1886 at the time it was a territory it wouldn't achieve statehood until three years later in 1889.
On the travel map, the northern half of Greece is shown as being part of Turkey. The Turks had been driven out of Greece by 1832, over 50 years before the movie takes place.
Sir Lionel mentions that Shangri-la have also been called Agartha. Although both mythical, Shangril-la and Agartha are two very different places: similar to the movie, Shangri-la is said to be a lost city in the Himalayas, home of the eternal youth. On the other hand, Agartha is a supposed mystical underground city, center to the theory of the Hollow Earth.