Other mistake: At one point, Indy rolls off of the side of a tank, and somehow gets a strap around one of the guns pointing out from the sides. The end of the barrel has already been blown open by the rock he shoved in earlier. How did the strap get around that big cluster of metal, and then back again so he could climb back on the tank? (01:34:15 - 01:35:05)
Other mistake: When they go under the coffin you see the flame of the torch in the background. How could the flame go under the petroleum with them without either setting light to the petroleum or being extinguished itself? (00:35:55)
Other mistake: In the catacombs, Indy flips over the casket with the skeleton and dives underneath together with Elsa. If you watch closely, the skeleton gets trapped inside the casket, however Indy and Elsa are alone inside the casket. If the skeleton had sunken, there wasn't enough time, nor did Elsa or Indy bump into it when they dove underneath.
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.
Other mistake: While Indy and Henry are aboard the zeppelin Indy tosses Vogel out the lounge window, and when Vogel shouts up to the departing airship, in the next exterior shot we see the zeppelin airborne against a scenic view. Later, when Indy realises the zeppelin is turning around it cuts to another exterior shot of the airship, and the scenic view is identical to the earlier shot, only it's been flipped. The images of the zeppelin facing two different directions were composited onto the same scenic background.
Other mistake: In the motorbike chase scene there is a lot of flying road dust even in front of the bike in the lead. Probably from the camera vehicle.
Other mistake: After Young Indy runs out of the cave with the Cross of Coronado, when he whistles for his horse and jumps down, note the horse's facial marking and leg marking. When Indy mounts the horse it's a different horse, note its markings, and as he rides toward the circus train the horse has changed again. (00:04:55)
Other mistake: Indy has been very careful to hide from everyone that Alexandretta is the city where the trail starts, only to give away all the essential info. He did not tell Elsa. Only Marcus (who has the rubbing of the crucial inscription) and Sallah knew. The only way that the Nazis find out is because he tells his dad, in a room which he KNOWS to be wired, i.e. bugged. (The Nazis also find the diary, but we know that the city isn't in there.) Stupidity doesn't quite cover it.
Other mistake: During the airplane chase Indy is seen firing his revolver at the German planes, after he crash-lands he pulls his revolver and breaks open the action to check if he's got any ammo left. He doesn't, but the issue is that a revolver doesn't eject spent shell casings, and there aren't any empty casings in his revolver, despite him firing his gun earlier and having no chance to empty the casings since.
Other mistake: When Indy is atop the tank with his father, he is facing his father. Suddenly, they show a close-up of Indy's face, head-on, with the Nazi leader behind him swinging a shovel towards Indy's head in the background. Indy gasps, and ducks. How did Indy see the shovel being swung at his head if it was completely behind him?"