Visible crew/equipment: As soon as Marion gets locked in the cockpit of the Nazi plane, you can see a crew, a blue van, a ladder, and a man with a white sleeveless shirt and a big brimmed hat all in the reflection of the glass. (01:18:20)
Visible crew/equipment: When Indy and Sallah are deciphering the head piece there is a shot over Indy's shoulder. As he turns you can see the reflection of a fluorescent light in his glasses. (00:48:40)
Visible crew/equipment: When Indiana is chasing the Nazis in the truck, look closely at the convertible, you can see the camera on the windshield. (01:23:25)
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)
Visible crew/equipment: At the beginning of the ark chase sequence, Indy jumps into a truck off a horse and fights the driver. He pushes the driver up against the door. At the bottom of the frame you can see the camera shadow. (01:23:35)
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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