Other mistake: At the beginning of movie when Indy is about to steal the gold idol, the camera does a close-up of it. The idol has been in a decaying temple for hundreds of years. but it appears shiny and new, as though just placed there. You'd expect the idol to at least be dusty or covered in jungle debris.
Other mistake: In the bar shootout, a man is shot in the head. The bullet hits him in his hat right in the middle of his forehead, and then his hat falls off. But we then see a close-up of his face, and there's no bullet wound in his forehead or anywhere else.