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

Continuity mistake: In the first scene of the procession, the Nazis are walking in a straight line along a path. In the next shot, they are now going around a curve.

Continuity mistake: In the Bantu Wind, the right arm of the soldier standing next to where Indy is hiding changes its position twice during Katanga's and Dietrich's speech. (01:36:18)

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: When the Nazis board the Bantu Wind, there are some shots of the pipe Indy is hiding in. During these shots, there's a big grey pipe right behind Indy's pipe. However, in the rest of the Bantu Wind shots, this grey pipe is on the left of Indy's pipe, not directly behind it. (01:36:19 - 01:37:05)

Continuity mistake: In Geheimhaven, Indy watches the submarine hidden behind some ropes. When Marion comes out of the submarine and the camera focuses on the back of Indy's head, the ropes disappear. (01:39:13)

Visible crew/equipment: When Indiana frees Marion, locked in the cabin pilot of the Nazi plane just after one of the soldiers is killed by the blades, a set light is reflected on the plane's glass. (01:20:32)
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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