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.
Revealing mistake: The Pan American aeroplane Indiana Jones boards in San Fransisco looks similar to (but has noticeable differences from) the Boeing 314 PanAm used for transpacific flights. This aeroplane did however not fly until 1938 and at the time of the story the company only flew transpacific with Sikorsky S-42s, an aeroplane with a completely different body than the one used in the scene.
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.
Factual error: When Indy flies to Nepal, there is a scene of the sea plane taking off with the Golden Gate Bridge in the background. The movie is set in 1936, and the bridge wasn't completed until 1937, with pictures from December 1936 showing large gaps still in the deck that do not appear in the movie. (00:23:00)
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.