
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)
Continuity mistake: As the Ark is placed on the altar, Toht moves to the left of Belloq. Behind the German, a soldier without cap can be seen filming with a hand-held camera. In the next shot, that soldier has moved to the opposite side of the canyon and is squatting. (01:44:24)

Continuity mistake: After the kliegs and generator explode, there is a shot of Belloq and Toht on the altar. Belloq has the ivory rod in a vertical position. In the next shot, the rod is horizontal.
Continuity mistake: When Indy and his excavation team arrive at the true location of the Well of Souls, we can see that it is on a low hill, just a few meters from the Nazi excavations. However, when it gets dark, we can see that the excavations have disappeared from view and now the Well of Souls appears to be on a considerably high mountain (taking as a reference the illuminated camp on the right of the screen).
Continuity mistake: Major Eaton's right hand moves from his ear to his mouth between shots. (00:17:34)

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)
Other mistake: One of the soldiers at the table Sallah and Indy walk next to, is only pretending to eat with his spoon. (00:54:53)
Continuity mistake: In the chapel, before Indy turns the chalkboard over to explain the staff of Ra and the medallion to the G-men, the chalkboard goes back and forth from tilting forward to tilting backward a few times.
Continuity mistake: When Toht frees Marion's arm, Dietrich enters the tent, and a few seconds later, Gobler enters. In the next shot, Gobler enters first, with Dietrich second. (01:07:52)
Continuity mistake: When Belloq and the Germans are at the Well of the Souls, a top-down view shot when Indy yells, "Why don't you come on down here and I'll show you!" shows Belloq and a German officer kneeling down to the left of him, also looking down into the hole. But the side view shots show only Belloq standing near the opening.
Continuity mistake: When Indy is listening to the one Army agent he is in the process of putting his right hand into his pocket. In the next shot the hand is back on the leather case. (00:16:46)
Continuity mistake: When the Cairo Henchman pulls the knife on Marion, the blade edge changes position from down to up to down again.
Revealing mistake: During the big car chase where Indy follows the ark, he comes down a hill on a horse to get into the truck. You can tell the ground has already been disturbed by the horse from previous takes.
Revealing mistake: After the German is chopped up in the propeller and the plane explodes, you can the blasting cord exploding along the path to the explosion.
Continuity mistake: During the truck chase, as Indy is fighting with the German driver, they knock over some scaffolding and a man drops down in front of the windshield. None of the workers on the scaffolding landed on the truck, much less the front of it. So, he shouldn't have been there.
Continuity mistake: In Indy's class at the beginning, the girl that lowers her eye lids to show the phrase "Love you", is looking in a totally different direction than the people behind her. They're all supposed to be looking at him, but the girls behind her are looking to their right while she is looking straight. They can't be daydreaming because they're all smiling and look infatuated. (00:13:58)
Continuity mistake: When Marcus enters the classroom he leans up against a wall and there are 2 girls in the front row next to him. When the bell rings, the girls are the first two students to leave the classroom. Seconds later when Indy looks over to Marcus the same two girls are just getting up from their desks.
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)
Continuity mistake: As the big German engages Indy in the fight, Marion is removing the chocks from one of the wheels. In the wide shot you don't see her at all, even climbing the plane to knock out of the pilot.
Revealing mistake: After Indy shoots the driver of the truck that Marion is supposedly in, the camera looks at the driver's bloody hand falling limp. In the shot of the truck tipping over, you see the stunt driver working the wheel.
Answer: Indy and Marcus Brody believed that the Ark needed to be studied. They certainly didn't want to put it back where it was found. They believed that the U.S. government would find the best archaeologists, researchers, and scientists in the world to study the Ark. They are both upset that instead, the government has decided to simply lock the Ark away. This is why Indy says, "Fools. They don't know what they've got there," as he is leaving the building.
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