Deliberate mistake: Polly's and Sky Captain's clothes are discarded because they are contaminated with uranium; however, Polly gets to keep her camera. Her camera would have been contaminated with uranium, too, because she had it with her in the underground cave.
Deliberate mistake: When the Neski file exchange takes place in the beginning, the Russian says "You can see who stole the money" and the camera shows the Russian documents. The documents (written in Russian), are in fact, a "Journal of Military Activity of Russian Army in April 1945." It is completely bogus and have nothing to do with the film. (00:07:15)
Deliberate mistake: When it starts raining so that "things couldn't be worse" according to Seth Green, the younger fat hillbilly pulls out an umbrella. Why would he have one when he is trying to hunt someone down and kill them? This was obviously put in for comedic purposes but doesn't play well in the movie. (01:05:40)