Continuity mistake: When Belloq talks to Indy in the Well of Souls the two Arabs on the left disappear in the angles from Indy's POV.
Audio problem: When Toht walks in with Dietrich and Gobler, watch the background, you will see Dietrich's lips moving, but you cannot hear him saying anything.
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.
Continuity mistake: Indy climbs on a plane's wing, and a German mechanic arrives and asks him what he's doing, raising his left arm and ordering him to approach. A shot later, the arm is down.
Continuity mistake: When Indy and Brody meet at the University with the two government officials, a group of rolled maps or plans are placed on a podium horizontally. Halfway through the scene, they are all laying vertically.
Continuity mistake: In the submarine dock of Geheimhaven, Captain Mohler is a man with dark hair in his mid or late thirties. But during the procession, he seems to be much older, with grey hair.
Other mistake: When Indy and Marion are sealed in the well of souls, they are completely cut off from the outside world. As such, other than the torches, it should be pitch black, but it is surprisingly well lit in there.
Continuity mistake: After the plane takes off in the beginning, Indy sees the snake. His hands are grabbing at it, but a second later his hands are on the rim of his cockpit.
Continuity mistake: When Indy is driving the truck with the ark, a German tries to get in on the right side. Indy kicks the door open twice, and after the second time the top hinge of the door gives easily. The guy is half way dragging on the ground, holding onto the now askew door. Then in the next closeup, the door is hung correctly with the guy on it, and Indy kicks it again. The guy goes dragging again, and then he and the door fall off.
Continuity mistake: There is a shot during the truck chase scene where a Nazi falls out from the back of the truck and goes through the windshield of the car behind it. During the shot from inside the truck, we see two Nazis to the left. The one closer to the camera pushes the other one down. However, in the very next shot, we see that pushed-down Nazi immediately sitting up straight.
Continuity mistake: When the temple collapses, Satipo is crouching looking at the chaos. Indy starts to run and there's a wide angle of the passage ahead but Satipo is nowhere around. He couldn't have managed to run that distance in half a second.
Continuity mistake: From the outside, the sides of the hole to access the map room are in shadows, from the angle inside they are sunny.
Continuity mistake: During the truck chase scene, the radiator bars Indy hangs onto keep swapping back and forth from bent outwards to slightly bent with no continuity at all.
Factual error: There's absolutely no way Sallah and Indy would be able to lift that 'lid' (for lack of a better word) off the ark. That thing is solid rock and would weigh close to a metric ton - and none of them look like professional deadlifters to me.
Factual error: When Indy is attempting to steal the Ark when driving the truck, one of the soldiers shoots him in the arm. Then another German punches him repeatedly in the same arm, causing Indy great pain and injury. After suffering a wound like that there's no way he'd be able to move that arm, let alone raise it above his head. But the next day after the boat is stopped by the sub, Indy jumps into the water and swims to the sub without any problems.
Continuity mistake: When Indy stands inside the Map Room, looking at the model of the city, the rays of the sun are to his left, and they move right and down as the sun rises. But since the entry hole is behind him, that would mean that the sun would be to the right when standing outside - but it was to his left when he entered the hole.
Continuity mistake: When the temple collapses, Indy is holding the idol with his right hand against his chest, and the left hand free and arm extended. A frame later, both arms are extended and holding the idol.
Continuity mistake: As Gobler's jeep is returning to the road after being hit by Indy, Gobler's goggles move from his eyes to his cap between shots.
Continuity mistake: When Dietrich and Toht look at the ghosts that pass behind them, the column of mist that is coming out of the Ark disappears.
Continuity mistake: Between the shots of Indy dressing as a Nazi and Captain Mohler reporting to Belloq and Dietrich, the Wurrfler appears to have advanced several inches forward (taking as reference the background behind the submarine, Mohler's location, and the fact that Belloq turns his head to the left to look at the Captain).