Revealing mistake: In the catacombs of the library, Indy and Elsa are waist deep in petroleum. Indy has a torch, and if you look carefully, you will see burning pieces of the torch fall and hit the petroleum. Wouldn't this start a fire as Kazim later on sets the cavern alight with a single match?
Revealing mistake: When Indy is breaking through the wall in the catacombs, and he uses his shoulder as a battering ram. You can see his head actually bounce off a piece of the rock real hard as he is going through the wall. If the rock was real, I guess Indy would have a lot to cry about that night.
Revealing mistake: Just a small detail. Watch the tank roll over the hill with the German officer holding onto the top. When the tank hits the ground, the turret pops off. The German soldier (the prop dummy) maintains its grasp on the turret and is pulled off with it. The sheer force of the crash would have easily blown a human body off the tank.
Revealing mistake: After Indy jumps onto the tank from the horse there's a shot where he stands up to face the bad guy if you look at the tracks on the sand behind him, they aren't caterpillar tracks but tyre tracks. The reason is that for the close-up shots a fake tank was built on top of a car, a security measure to avoid anyone getting hurt in case they fell off.
Revealing mistake: When fire sweeps through the catacombs under the church, you can see that the "rats" are completely fake. At the far left of the screen (widescreen) you can see several fake rats just hanging on the wall and not moving at all. In the "special features" section on the DVD, Steven Spielberg admitted that the rats were fake - he couldn't bring himself to roast live ones so he could not make this scene appear realistic.
Revealing 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.