Continuity mistake: When Indy uses his whip to swing into the mine cart that Willie and Shorty are in, the way that he is holding the whip changes from shot to shot. Frontal shots show Indy holding the whip with his hands above his head. In shots from behind, Indy is holding the whip with his hands at his chest.
Continuity mistake: Before the water tank falls, there's a shot on Mola Ram and his people next to it. Then there's a wide shot of the tank about to burst and the people running away from the area. Then the previous shot of Mola Ram standing calmly with his men by the tank is repeated, which makes no sense.