Factual error: There's absolutely no way Sallah and Indy would be able to lift that 'lid' (for lack of a better word) off the ark. That thing is solid rock and would weigh close to a metric ton - and none of them look like professional deadlifters to me.
Factual error: When Indy is attempting to steal the Ark when driving the truck, one of the soldiers shoots him in the arm. Then another German punches him repeatedly in the same arm, causing Indy great pain and injury. After suffering a wound like that there's no way he'd be able to move that arm, let alone raise it above his head. But the next day after the boat is stopped by the sub, Indy jumps into the water and swims to the sub without any problems.
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.
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.
Continuity mistake: When the Wurffler arrives to Geheimhaven dock, six soldiers and an officer are running towards the submarine. In the next shot, the seven men have disappeared.
Visible crew/equipment: Just before the shooting starts at The Raven, you can see that Otto's shadow movements do not match the German's movements. Also, when Marion fights with Toht, behind her you can see the shadow of a man with short hair and no hat moving to the left (Indy still has his hat on during this scene).
Continuity mistake: On the blackboard, between the numbers 4 and 5, the word "and" is written. After the girl shows the "Love you", the word is replaced by a dot. (00:13:49)
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: During the procession scene, in the shot before Toht takes off his hat, about twenty soldiers can be seen walking. After Indy leaves the procession and hides behind a box, in the next shot, there appear to be twice as many soldiers as in the first scene. Just before Indy shouts "Hello!", the quantity has returned to twenty.
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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