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)
Continuity mistake: In the scene where Sallah and Jones are in the Well of Souls where they are putting the sticks in the Ark to left it up. Notice Sallah stick, when he first puts it in, on the stick are no tassels. But when they both left at the same time Sallah same stick that he put in has tassels on it.

Continuity mistake: As Indy and Satipo enter the temple, When Indy says to Satipo "stop" he is holding the whip in his right hand, yet when Indy says "stay out of the light" the whip is in his left hand. (00:05:10)

Revealing mistake: Just before Belloq says "beautiful", look carefully at the woman's ghost in the center of the screen. You can see one of the wires on her back that makes the stunt woman fly, a black line above her left shoulder.
Continuity mistake: The fight scene in Marion's bar clearly shows Indy using an automatic pistol to shoot at the bad guys. You can see the slide lock open when he runs out of ammo. But when the scene switches he is holding a revolver. Then when the huge guy is strangling Indy and the German says, "Shoot them, shoot them both." Indy is once again holding an automatic.
Audio problem: Watch and listen when Marion is being held prisoner in Nepal by one of the thugs. As he seizes her, she's grunting in strain/pain. We can see this in the first, frontal shot of them. However, in the following side shot (from slightly behind Marion as Toht walks over with the heated poker), Marion's mouth is completely still and almost shut, yet her sounds continue (and these sounds would have to be made with wide-spread lips).

Continuity mistake: During the scene where Indy and Marcus are with the Army intelligence agents, watch the agent who is wearing the light blue suit - at the moment when Marcus refers to a secret chamber, the agent in the blue suit has his right hand resting on top the chair that he is sitting on, but in the next shot when he replies "secret chamber" his right hand is now on his face. (00:17:55)
Factual error: The captain of the Bantu Wind, Katanga, wears a hat that originated from the Yugoslav People's Navy. But the Yugoslav Navy wasn't formed until 1945, 9 years after this movie takes place.
Factual error: During the fight scene at the German flying wing, the pilot ducks into the plane and pulls out a pistol and cocks it. The pistol is a P38 9mm semi-auto that the Germans did not issue until 1938, two years later.

Continuity mistake: When Indy is packing his suitcase to go to Nepal, he picks up a gun that is wrapped in a piece of cloth, he tosses the gun with his left hand into his right hand and begins to unwrap the gun from the cloth by raising his right hand, so that the gun will fall into his left hand, but the gun ends up falling into Indy's right hand instead of his left hand. (00:22:10)

Continuity mistake: When Indy is deciphering the object with the old man, there is a telescope behind them. It changes orientation between shots. (00:48:15)
Continuity mistake: As Indiana writes "Neolithic" on the blackboard in his classroom at the beginning of the movie, he stops and checks to see if he's spelling it right, then finishes writing it. Later shots of the board reveal the same word on the board, only either the handwriting is different or the actual structure of the word has changed.
Continuity mistake: When Indiana is climbing the statue to escape from the Well of Souls, the snake he encounters makes a rattling sound. However, the snake has no rattle and rattlesnakes are indigenous to the Americas. (01:13:40)
Factual error: When Indiana Jones ambushes the Nazis with the Ark, he threatens them with an anti-tank rocket. This is set in 1936, and anti-tank rockets weren't developed until the American M1 in 1942. The Germans immediately copied it from captured weapons and made their own much larger version known as the Panzerschreck, then Panzerfaust. The Russian RPG which Indy is holding was developed from the Panzerfaust in 1949. (01:41:55)
Continuity mistake: In the map room, Indy pulls out a notebook and takes off the elastic band. The elastic goes flying away. Moments later he closes the book and the elastic is in his hand. Also, the elastic starts off being pink (the one that flies off), then blue (the one that he puts back onto the book) and ends as tan coloured when he puts the book back in his pocket.
Continuity mistake: While Indy is fighting the German who is driving the truck, you can see that the German has got blood on his left hand, but when he throws Indy through the windscreen his left hand is clean and there is no blood on it. (01:27:10)
Revealing mistake: When Indy is fighting the big German at the plane, if you look at the wheels when the plane is turning around, you can see a chain and sprocket assembly that is driving the wheel to actually turn the plane. (01:18:55)

Revealing mistake: After Marion goes in the basket, there is a chase and a truck tips over, if you look amidst the dust, you can see the ram used to put the vehicle on its side.
Continuity mistake: When Indy is in the map room, he blows sand away from a hole and a bunch of hieroglyphics, but in the next shot, there's sand scattered all over the stone he just finished clearing away. (00:52:10)
Plot hole: Indy stows away on the Nazi sub on the way to the secret Nazi base somewhere near Greece. Where did he stay all that time? Inside? On a VII-Class boat, there's barely enough room for the regular crew, and hardly any places to hide. Also, everybody knows everybody, so no passing yourself off as "the new guy." Outside then maybe? Well, the boat did dive, it's in the dialog, and while on the surface, German U-boats always had a bridge watch on the tower, so no luck there either. Note that by all accounts I could find, German submarines were required to always post a bridge watch, if only because otherwise they would be running essentially blind. It's not like the helmsman's station in the tower had any windows.
Answer: I also remember this scene. After the ark is sealed, the camera performs a close up of the side of the crate. The stamp reads "Top Secret Army Intel 9906753 Do Not Open" This stamp is burned off just like the swastika is in the scene on the submarine, because in the eyes of God, no nation is holy or worthy enough to claim ownership of the ark. However, this final scene was cut (the burning of the stamp) from the film for a variety of unclear reasons. While it was in theaters, this scene was not included on the DVD version.
Add me to this. We saw the movie in a "pre release" version in Orlando Florida. No advance warning of the movie. We went to see another flick and at the end were "invited" to see this if we were willing to critique it afterwards. This scene was included. I also always wondered why the change.
I also remember seeing this mysterious 'burning' of the logo, most likely it was on a VHS copy of this movie. Yes, it did exist.
I saw it in former Czechoslovakia in the second half of 80's in cinema (west movies came to the east countries' cinemas years later). And I thought it was a great joke that burning out the swastika wasn't just because the Nazis are bad but because nobody is great enough to own the arc. Then after the Velvet revolution I saw the film again on TV (beginning of 90's) and said everyone around: watch it until the end, wait on the post-credit scene, there will be a surprise.
And there was a surprise. The scene was cut off! I was angry on the TV they didn't show the scene. I cannot be influenced by internet discussion or urban legend. The internet didn't exist yet.
I saw it in Portland, Oregon, and was so impressed with the message it carried, that I told friends and we went several times just to see it. Funny thing was when I mentioned it a few years ago, many people said I was a LIAR that it never happened. I could not convince anyone. It was removed because it wasn't Politically Correct. USA is a force for good, God would not burn off AMERICAN TEXT! BUT WE DID SEE IT. Thanks to our Australian eye witness, we know we did not imagine it.