Trivia: A German sentence which could be counted as a mistake: When Indy and company are taken by surprise and captured by the German troopers in the Grail temple, one of them shouts, 'Das ist ein Überfall' (it's the last sentence before the group is brought before Donovan and Elsa). This actually means, 'This is a robbery'. I can't tell, though, whether the script writers consulted the wrong material or if this is considered to be an inside joke for linguists.
Trivia: While in the Zepplin Jones Sr. comments on not having his glasses on. If you look carefully the paper is upside down.
Trivia: Not a mistake, but a translation. During the fighting scene on the tank. Indy is punched and hits the periscope while the solders inside watch. One of the solders says to the other "The Americans - they fight like women" in German and then gets hit by the periscope. Funny scene as it is, but better if you understand German.
Trivia: During the scene with Hitler in Berlin, there is one shot where some books to be burnt are shown. If you look closely, you can see that one is "Das Kapital" by Karl Marx.
Trivia: Indiana Jones does not like being called Henry by his father (his proper name) and tells his father to call him Indiana. Prof. Jones replies with, "We called the dog Indiana". George Lucas created the character of Indiana Jones and he named the character after his pet Malamute dog, Indiana.
Trivia: The beach scene where Indy's father frightens the seagulls into taking flight and bringing down the Messerschmitt was done with fake seagulls and real white doves. The beach was covered with fake seagulls for the wide shot, and the closeup shots were done with white doves and piles of loose feathers to further confuse things. The film crew had to use white doves because it turned out that they absolutely could not train live seagulls to do anything at all on cue.
Trivia: When Indy elbows Marcus off of the tank, watch the centre of your screen. A few shots later, you can see Marcus between Indy and Connery. For about one second, it looks like Marcus is laying flat on his back and a second later, he raises his legs into the air. It just doesn't look right but is extremely hilarious to watch. (01:35:35)
Trivia: On the zeppelin, the Nazi shows around a flyer with Dr. Jones Sr.'s picture on it. At the second table, a woman shakes her head 'no' before even looking at the picture. Possibly just the character not bothering to pay attention, as could happen in reality, but worth looking out for.