Factual error: When Hitler signs the diary, he writes in a modern way of writing. But in the late 30s there was a different style of writing called "Suetterlin". The letters looked quite different from nowadays. (01:10:25)
Continuity mistake: When Indy gives his father water from the grail to drink, the grail glows from inside, and the gold inside it is bright and even. But when Indy pours water over the wound, the grail is dark inside and there are dark patches in the gold. Obviously, they had to take the light that made the grail glow out so it wouldn't be seen when Indy pours the water over his father.
Revealing mistake: When Kazim dies, his shirt is all bloody, but there are no holes in it. The bloodstains looks painted on. (01:26:30)
Continuity mistake: The 109s that are animated are shaped like the original German fuel injected ones. The shots where it's a real plane show the modified one with a RR Merlin engine that gives it a weird square nose.
Continuity mistake: As Sallah pulls Dr. Jones senior off the tread of the tank, Indy lets go of his whip and turns towards the German colonel and they continue fighting face-to-face. You can see that Indy punches the colonel so that he loses his balance and stumbles backwards. A split second later, the colonel is standing behind Jones with his arm around Indy's neck. They did not have nearly enough time to so radically change positions. (01:32:15)
Other mistake: When Indy and Kazim are fighting on the the boat as it is being chewed up by the giant propeller, the propeller is more than half way out of the water; if the ship was in dry-dock the smaller boats wouldn't be able to go up to the larger ship, on the other hand if it had run aground it would not be running its engines.
Continuity mistake: When Indiana pushes the Nazi colonel out of an open window, if you look carefully, the colonel fell a few metres out of the zeppelin before landing on a pile of suitcases, but when the colonel looks up, the zeppelin is several hundred metres above him, in too short a time to ascend that much.