The elephant used in Bali is different one since the one in Bali has an orange mark on the right side of its body. The elephant in Bali is also smaller.
When Allan, Julius, and Benny leave the filling station, the door to the gasoline tank is open. After they stop, argue, and finally pull away, the door is now closed.
Elephants cannot sit down as depicted in the movie. The trick was done using a fake elephant's bottom.
In the movie, when Allan meets Truman during the Trinity Test, Truman is the Vice President and FDR dies shortly thereafter.
In reality FDR died several months earlier and Truman was president well before the test.
When Allan knocks the first crook over, it takes the crook about half a second to react to the blow.
When Alan is part of the skyscraper construction crew in New York, his workmate was highly unlikely to know even of the mere existence of the Manhattan Project, let alone know what its real purpose was.
In Allan's voiceover, while telling about the Russian doll Allan's father brought him once to his birthday he is calling it "Babushka". The Russian name of these dolls is "Matrjoshka", but in Scandinavia they are often called "Babushka" (Russian for Grandmother). (In the English subtitled version, in which the voice overs are dubbed into spoken English by a different actor, this is corrected to "matrjoshka.")
Allan,The Swede who learned to speak Spanish English and Russian always speaks with the German Herbert Einstein in English. The fact that Allan can already speak two Germanic languages (Swedish and English in this case) would make it very easy for him to learn and speak German to converse with Herbert.