Continuity mistake: Short falls through the hole and there's a POV shot of his legs moving wildly while he cries "Help!" Then he is rescued by Willie and lifted up safely, his legs now still, and his nerves calmed. However, the very same shot of the wild legs and the cries for help from before is suddenly inserted, which makes no sense whatsoever.
Continuity mistake: In the mine, Indy fights against a bearded bad guy, who throws a hammer backwards that lands on a worker's head, knocking him out. The workers are very close together in the wide angle, then equidistant in the close-up when the hammer lands, and then together again in the wide angle. Also the worker that falls unconscious is standing straight a frame later.
Continuity mistake: When Indy is fighting the Chief Guard on the conveyor belt, there is nothing behind the guard before he picks up the large rock, but in a close-up there are now small rocks on the belt.