
Continuity mistake: Over Belloq's left shoulder and behind Toht, a soldier stands next to a klieg with a machine gun. In the next shot, the soldier's gun has disappeared. (01:44:25)

Continuity mistake: When the two soldiers place the Ark on the altar, they move to the walls of the canyon, and Toht stands next to Belloq. A few shots later, the soldiers are next to the Ark's poles (where they will be in the next shot), and Toht seems to be very huge. (01:44:39)
Other mistake: The Angel of Death attacks the altar and Toht and Dietrich scream because of its revelation, but Belloq, for some reason, doesn't seem to see it. Just before the fire column rises, he's still calm. (01:47:10)
Suggested correction: If you don't know the reason, perhaps you should ask a question instead of assuming it is a mistake. Belloq studied the ark and probably better predicted what might come out of the ark. He is also looking directly into the ark and is mesmerized by what he is seeing, until eventually he does scream before his head explodes. The other two are terrified at seeing the apparitions.
Actually, it's pretty impossible that Belloq studied the Ark. If he knew what would come out of it, he literally committed suicide by opening and watching the Ark open, which doesn't make sense. He believed during the whole movie that the Ark contained the Ten Commandments tablets, not some kind of ghastly things.
He didn't know what would come out, but it doesn't mean that he, like Indy, expected just 2 stone tablets. He expected power, for him mostly.

Revealing mistake: When the Nazis are about to glow (and die), check the one on our left. His shirt is already unbuttoned right where the light will subsequently glow (which was a mere light bulb). A second later, he triggers a device clutched in his right hand (seemingly a switch) seconds before his chest lights up. (01:47:25)

Continuity mistake: While the Holy Fire is killing the soldiers, in a shot of two soldiers being hit by the light, the stone wall is missing in the background of the scene. (01:47:30)

Visible crew/equipment: Right when the Nazis are struck with the light, one soldier shakes wildly and one can see the cable coming out of his trousers and stretching off-screen to the right. (01:47:30)
Continuity mistake: Indy and a Nazi soldier are fighting in the cab of the truck when they come to a place where a stone building is being built. As the truck is driving into the scaffolding, several rocks come down and hit the truck and remove the rack from the top. Moments later the rack is back in place. (02:50:00 - 03:01:00)
Revealing mistake: While Indy and Marion are in the Well of Souls, and they encounter the snakes, Indy falls to the ground only to be confronted by a hissing Cobra rearing its head. Look carefully and you'll see the snake's reflection on the safety glass between it and Indy. Briefly you can also see the torch's reflection while he's waving it around. You can also see Marion's reflection when she falls in later on and is face to face with the cobra. [This has been corrected in the new DVD set. You can only see it if you have the original VHS. I think it's visible in the "making of" on the DVD as well.]

Continuity mistake: When Indy is distracted by the young girl and her eyelid message, the girl changes from a window seat to another row when the bell rings to end class.
Revealing mistake: After Indy gets behind the wheel of the truck containing the ark, he jerks the steering wheel to the right to run the pursuing jeep off the road. He then jerks the wheel to the left to hit an upcoming motorcycle. In neither case do you see his body sway with the presumably drastic swerve of the truck. Apparently this was filmed in a stationary vehicle, or one in tow that was fitted with a prop steering wheel.
Revealing mistake: When Indy jumps across the pit to pursue the spy that took the idol, he barely makes it across, grabbing the ledge on the opposite side with his hands. When he pulls himself up, he kicks loose a rock and the entire "solid" rock wall shakes like it's nothing more than a foam wall.
Continuity mistake: When the village crowd separates and reveals a standoff between Indy and the black-robed swordsman, the rear shot of Indy shows his hip-bag to the rear of him, the frontal shot of Indy shows his hip-bag on the forward part of his hip.
Factual error: When flying from Nepal to Egypt Indy passes over Arabia. The state of Jordan is shown, but in 1935 Jordan was called The Emirate of Transjordan.
Continuity mistake: Marion's bar in Nepal is built with thick stone walls, but after the fire, all you see is the burned-out shell of a wood-frame building.
Factual error: It should be a tricky task to put an object the size of the Ark on board a German VIIC submarine; perhaps you can find enough place inside but how do you manage to introduce that bulky case through the narrow hatches of the sub? Even the torpedo load hatches were just a little more than 21 inches in diameter.

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?
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.
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.)