
Continuity mistake: Just after Indiana (barely) escapes the tumbling boulder at the beginning of the movie, he leaps through a veil of spider webs, only to be held up by the native hunters and Belloq, who takes the idol from Indiana. Watch carefully - there is a thick strand of webs attached to the idol as Indy hands it to Belloq, but they disappear in the next shot as Belloq hefts the idol and holds it up in the air.
Factual error: Indy's satchel is a Mk VII gas mask bag, which was created for use in World War II, so it didn't even exist at the time the film takes place (1936). The similar Mk V existed at the time, though.
Revealing mistake: Where is all the light coming from in the Well of Souls, even after the entrance was re-sealed, and the only torch still burning went out?
Continuity mistake: When Indy and the Peruvian are entering the cave and clearing the cobwebs, you can see at least one spider on Indy's back. The next shot shows a clear, long shot of Indy's back with light reflecting on his jacket and no spiders. In the next shot, the Peruvian notices the spiders. (00:04:20)

Continuity mistake: When the government comes to see Indy at the University he is teaching, they enter the large room, I think it's a gymnasium. He puts the huge book on the table and one of the buckles comes undone. But when he goes to open the book to show the g-men a picture of the Ark he undoes both buckles. (00:15:30 - 00:19:30)
Factual error: At the beginning of the movie, when Indiana is looking for the temple, you can hear a bird call. It also can be heard when Indy is running from the natives. The bird is a willow ptarmigan. It lives in very cold areas in the far north of North America. Even a very directionally-challenged ptarmigan could not possibly end up in South America. You can also hear the unmistakable laughing sounds of the kookaburras, only found in Australia.
Factual error: The film starts in the year 1936, and just like the RPG Indy uses to threaten Belloq with, the MP40s (or at the earliest, MP38s) are an arms-historical anachronism in this movie. As the numbers in their names imply, the MP38 was first produced in 1938. The weapons in the movie are not the similar-looking ERMA MP-36, you can see the ribbed, vertically angled magazine holders typical for the MP40 - its predecessors had either a 30°-canted, smooth magazine holder (MP36) or a round viewing port for checking the ammo (MP38). (01:31:45)
Continuity mistake: At the beginning of the film, Indiana Jones uses his whip to disarm a man with a handgun. The scene showing this action includes several quick shots, but as a result of the use of these multiple shots it can be seen that the whip descends twice. (Slow motion helps, but isn't required.)

Revealing mistake: During the truck chase scene, Indiana is thrown or forced over the front of the bonnet and almost run over. There is a wide camera shot, and while holding on to the front fender, Indiana can be seen sitting on a chair which is attached to the truck. (01:27:40)
Continuity mistake: In the beginning, Indy's partner takes the idol, throws down the whip, and leaves him hanging on a ledge with the ceiling closing down to the ground. While he is hanging the you can see that the ceiling barely has enough room for Indy to fit. Indy struggles to get up which during this time he would have no room to get under, yet when he finally gets up the ceiling has risen giving him plenty of room to get under. (00:08:45)
Continuity mistake: When Indy and the German driver crash through the villager's construction ladders the truck is missing the Mercedes-Benz hood ornament that appears in every other shot.
Continuity mistake: When Indy is climbing into the map room, he throws the staff of Ra down the hole, yet when he climbs down, it's resting perfectly against the wall, as if someone had placed it there. (00:50:40)
Audio problem: When the monkey is crawling on Marion's head at Salah's place, the sound does not match Marion's mouth.
Continuity mistake: In the scene where Indy is telling about the Staff of Ra, the background color of the blackboard changes between shots. It looks like there are some chalk residues (after the blackboard has been washed) in one of the shots, but not in the other.
Factual error: The German submarine that Indy stows away on has the number 26 on its side. The U-26 was a Type IA U-boat (it came into service in 1936 and was sunk in 1940), but the sub in the movie seems to be a Type VIIB or VIIC. It's true that the two types looked fairly similar, but they were different classes of U-boat.

Continuity mistake: When Indy is being lowered into the map room, the exterior shot of the opening does not match the interior. From the outside, the wall around the opening is a lot thicker. The angle is also different. (00:50:55)

Continuity mistake: Sallah and Indy are peering into the well of souls. Sallah is to the right of Indy. Indy then drops the torch into the well, and when the camera comes back up, Sallah is on the left of Indy. (01:00:00 - 01:00:45)
Suggested correction: Indy and Sallah spent several seconds off-camera, enough to move around the hole and switch places.

Continuity mistake: When Indy is trying to stop the truck that is supposedly carrying Marion in a basket, Indy shoots the driver as the truck heads towards a "dead end". The driver's foot hits the accelerator and the next shot opens up to a big open space where the truck tips over and explodes. The "dead end" has disappeared. (00:40:10)

Continuity mistake: The stone block Indy pushes out to create an opening which allows him and Marion to escape the Well Of Souls apparently rolls down the hill outside. We see it, in a following scene, laying about 15 feet away from the Well. But when Indy is fighting the big German guard near the airplane, one scene clearly shows the Well in the background and the dislodged stone is now laying on the hill only a few feet from the opening. (01:15:45 - 01:18:10)
Continuity mistake: When Sallah lowers Indy into the Map Room, from the outside Sallah is standing near the bottom of the hole, but from the inside the rope hangs from near the top. (00:50:55)