Character mistake: When the crew of the German U-boat boards Katanga's ship, the submarine moves in a position perpendicular to the ship's bow as if to block its path. In reality, this would have been a pretty stupid move by the German captain, as Katanga could have rammed the submarine easily. Any kind of damage to the hull, especially ramming damage (even from small ships), would have been catastrophic to the submarine. It makes no sense to make a manoeuvre like this.
Factual error: The captain of the Bantu Wind, Katanga, wears a hat that originated from the Yugoslav People's Navy. But the Yugoslav Navy wasn't formed until 1945, 9 years after this movie takes place.
Continuity mistake: After hitting one thug, Indy jumps out of the way of one trying to spear him, leading to the one behind Indy getting run through. As the guy gets run through, he is in front of a hanging string of fruit, with the stacked fruit to his right. After a cut scene to Indy and Marion running away, the run through thug is now facing the fruit stand, setting up the sight gag of the blade sticking out with two fruits stuck on it.
Continuity mistake: When Indiana is hiding his face with the cloth, watch as he enters the tent that Marion is being held prisoner in - at first, Indiana has to hold it in place; in the next shot, he has it tucked into the rest of the folds. The next shot, the actual position of the cloth changes.
Continuity mistake: When Indiana is fighting the Big German mechanic by the plane, the plane goes around in circles and the wing tip of the plane punctures a hole in a petrol tanker that is parked near by. This causes the petrol to gush out of the tanker and you can see that ground underneath the plane gets totally drenched with petrol. But in the later shots, the ground under the plane is dry. There is also a shot where you can see the tanker in the background not pouring petrol any more and all you can see is a little wet spot around the tanker. (01:18:45)