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: 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: 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: While Indy is in the Well of Souls, Belloq greets him and is standing by one of the four sides of the rectangular hole. A frame later he stands by one of the corners.
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: When Indy is in the map room, he clears off the slot where the staff is supposed to go, right in front of a jagged line. However, in the split-second shot of the staff being inserted, it's not in the same hole. It's a bit to the left.
Visible crew/equipment: After Marion gets locked inside the flying wing's cockpit, she sees the truck with soldiers approaching. Marion then goes through the aircraft's passageway to the rear turret, and in the first shot facing Marion just as she begins to fire on the soldiers with the tail gunner's machine gun, the reflection of a crew member wearing a short-sleeved shirt is visible on the dome's glass, at the bottom left corner of the screen. (01:18:40)
Other mistake: During the scene when Belloq arrives at the Well of Souls, the poles to the Ark can be seen leaning up against the crate whenever the shot is from outside the Well of Souls. When the shot is from Indy's point of view, looking up and out of the Well of Souls, the poles are missing from the scene.
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)
Continuity mistake: As the Nazis are preparing to leave Tanis, a soldier fires a shot into the air, causing several Arabs to fall to the ground and land in the middle of a circle of soldiers. In the next shot, as Belloq heads for the car, all the downed Arabs, the sergeant and the circle of soldiers have disappeared, with only the soldiers who were loading the Ark onto the truck remaining. (01:26:55)
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).
Other mistake: In a shot of Belloq speaking to Indy in the Well of Souls, in some shots of the Desert Chase (such as when Belloq shouts Allah va!) and when the three villains enter the submarine with Marion, Wolf Kahler's double is seen, who has black hair. (01:10:43 - 01:24:42)
Continuity mistake: In the shot after Belloq's death, the generator and the rock Indy and Marion are on disappear.
Continuity mistake: Eaton and Musgrove are sitting, waiting for Indy to open the book. When Indy opens it, suddenly Musgrove is standing. (00:19:43)
Continuity mistake: When Indy abruptly brakes the truck and the Ark box slides backwards, the poles on either side of the box disappear for the rest of the chase.
Audio problem: Just before Belloq opens the staff car's door, Paul Freeman's voice can be heard saying "Let's get out of here" but Belloq's lips don't move.
Continuity mistake: When Marion gets off the submarine, there are two soldiers behind her. In the next shot, one of the soldiers has disappeared.
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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