Factual error: Several times during the movie, Indy is under fire from Nazis or other bad guys wielding what look like MP-38 sub machine guns. The movie is set in 1936, 2 years before the weapon was even designed. The Erma EMP-36 has wooden parts (the grip), the muzzle spike at under the barrel is more pointy and the front sight are more massive than MP-38/40, and the magazine is tilting slightly forwards towards the muzzle. The MP-38/40 is all stamped sheet metal (no wood, because it would slow down production), the muzzle spike under the barrel is more smooth (maybe so it won't get stuck?) and the front sight is more simple (basically just a ring with rumble strips) than the ERMA's, and the magazine on the MP-38/40 is vertical.
Continuity mistake: After Indy replaces the idol for a bag filled with sand, the position of the bag changes between frames.
Other mistake: During the truck scene, after the German officer hanging onto the door falls down and another guy crawls over the roof, palm trees are reflected on the windshield, but wide shots show not a single tree around because the palm trees area was left behind a while ago.
Continuity mistake: In the map room, after Indy has discovered where to put the stick in, the sun rays lights the head and shoulder of a painted figure and the whole body of the figure to the right of it. A frame later the first figure is now completely lit. Too fast a change.
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.
Continuity mistake: After Indy rips a big strip of Marion's dress in the Well of Souls, it continues to change until she finally gets rid of it on the boat. At some points (eg. running from the plane before it explodes, and other shots) it seems quite straight across, more like a shorter dress than a torn one. A few moments later, when they are crouching behind an earth bank and Sallah tells Indy the Germans are putting the Ark on to a truck, the dress is badly ripped in various places across her back. Not long afterwards, it is in one piece again but back to the bottom edge being ripped. (01:13:00 - 01:21:35)
Continuity mistake: When Indy climbs onto the pontoon of the airplane from the lagoon in the opening sequence, he is obviously wet from swimming in the lagoon. However, in the next scene as he climbs further, his clothes are miraculously dry as observed by watching them blowing freely during take-off. (00:12:05)
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 officer arrives and asks him what's he doing, raising his left arm ordering him to approach. A frame 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.
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.
Revealing mistake: When Belloq's head explodes, the actor has been visibly replaced by a dummy.
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.