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: 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.
Continuity mistake: After grabbing the idol, the cave starts to collapse, filling the place with rocks and rubble. When Indy starts to run, from the angle behind the floor is clean, rocks starting to fall for the first time.

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.
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: When the portal opens over Geheimhaven, you can see that in the sky and inside the portal there are a lot of blue clouds. Two shots later, in the shot inside the portal when the fire turns on itself, the clouds have disappeared and the portal's interior is now the normal night sky (black and with one star visible).
Continuity mistake: When the Ark is 'sucking' all the fire, the klieg on the left of the screen points towards the altar. Two shots later (and after the Ark closes), that klieg points towards Indy and Marion.
Continuity mistake: Just as the ghosts fly out of the Ark, a soldier can be seen on the left side of the altar, with nothing in his hands. Two shots later, that soldier is now carrying a banner.

Continuity mistake: As the ghosts dance around the pole to which Indy and Marion are tied, large clouds can be seen in the sky behind them. However, after a ghost circles Dietrich and passes in front of the camera, it can be seen in the background that the clouds behind Indy and Marion have disappeared.

Continuity mistake: As the ghosts dance around Dietrich, Belloq, and Toht, the Frenchman slowly looks up as the column of mist ascends upwards from the Ark, almost looking straight ahead. In the next shot, Belloq is looking down again; the shape of the mist has changed, and the column of mist is now moving to the right.

Continuity mistake: While the Ark is killing the soldiers, the cameraman is hit twice, as the first hit is shown in the first wide shot of the dying soldiers and the second when the camera focuses on the cameraman. Also, during the second hit, a beam passes through the camera and strikes the cameraman in the face, although he remains standing. In the next shot, the cameraman's body is suddenly on the ground and the beam that had killed him disappears.

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).
Continuity mistake: As Dietrich, Toht, Belloq and Marion board the Wurrfler, a naval officer descends the ladder and turns, his back to the ladder. In the next shot, he is facing the ladder.
Continuity mistake: The Angel of Death, judging from the position of the lid of the Ark (the two angels can be seen below the ghost), is located just above Dietrich's head. However, Toht screams as if it were right in front of him and Dietrich as if it were in front of Belloq (judging by their looks).

Continuity mistake: The distance between Otto and the Nepalese changes between shots, just as Toht begins saying "Surely he told you..."
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.