Visible crew/equipment: When Indy is on the rope bridge at the end, his sword keeps reflecting the white lights being used to illuminate the scene. The sun wouldn't be at the angle he's reflecting as it would be up in the sky, not behind the camera where this light source is.
Other mistake: When the airplane Indy and company are flying in runs out of gas, there is a close up of the instrument panel. The hands of the altimeter start spinning as the plane descends. However, so does the altimeter setting at the side. The altimeter setting is changed by the knob at the bottom. It does not change with altitude.
Revealing mistake: When the water floods the mine, some shots of the 3 heroes are an obvious composite of their blue screened image over a set. Problem is, when Indy tells the two to run towards a tunnel on the right with a log blocking the way, Indy and Shorty run through the log as if they were ghosts.
Factual error: They escape from the plane using a life raft and fall a considerable distance (looks like hundreds of feet) before landing on a snowfield. They then slide down the snow and off a cliff before landing in a fast flowing river, again falling a considerable height. There is no way they would be able to fall that distance and land on snow covered ground or a river without being killed or seriously injured, but they are completely unscathed.
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.
Revealing mistake: When Indy is hanging on the cliff as it falls out from underneath him (right after the mine cart scene), as he's kicking, you can see the stone wall moving in and out as he hits it after the rocks fall out underneath him.
Continuity mistake: At the start of the mine car chase look at the length of the braking poles on the side of the car. When they leave the main cave the roof lowers and the braking poles are slightly higher than the side of the car but were a lot longer to start with.