Other 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.
Continuity mistake: When Indiana is confronted by the Cairo swordsman, he already has his left shoulder pointing towards his opponent in the shot where the crowd scatters. But in the following shot, where the swordsman is first seen, Indiana has his right shoulder pointing forward and is just turning around to his left side. (00:40:14)
Continuity mistake: While escaping from the boulder, right before the spiderweb scene, Indy runs facing forward and makes a right turn. A shot later from a wide angle he is facing backwards.
Continuity mistake: When Indy is driving the truck, chasing Belloq and his Nazi cohorts, the last Nazi guarding the Ark of the Covenant climbs to the driver's side of the truck and kicks Indy away from the steering wheel. The first time he punches Indy in the arm, Indy's blood is on his fist. However, the second time he punches Indy in the same spot, there is no blood on his fist.
Visible crew/equipment: When Indiana is thrown through the windshield of the truck during the truck chase scene, there is another man in the driver's seat leaning toward the door, driving the truck with dark hair. This is noticeable just as the glass is broken.
Visible crew/equipment: As the bad guys are leaving the dig site for Cairo, there is a shot of the black vehicle (lead car) looking right at the driver. On the bottom of the shot is a shadow of film equipment that shouldn't be there. The shot lingers, so the shadow is very visible. (01:22:50)
Other mistake: In the opening scene Indiana is with horses and scouts. A few minutes later he is running for his life and in a few moments he's at a waiting plane. Why does he need scouts and horses for the cave is in walking distance from the plane and how did the scouts and horses get there?
Character mistake: Watch the extras playing the Cairo civilians walking around just before the big swordsman reveals himself to Indy. Several of them are just aimlessly walking back and forth as if they have no idea where to go.
Continuity mistake: Arnold holds a hot stick of metal to Marion's face in her bar, threatening her. In the opposite angle, the metal is nowhere to be seen when it should be right next to her face. Cut back to the other angle and we see it again.
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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