Continuity mistake: After the guy with the patch and the monkey greets the Nazis, Marion and Indy are seen walking through town, passing by an arched door. A frame later, from a different angle, they are passing by again and the amount of people around has increased.
Continuity mistake: In the marketplace standoff between Indy and his would-be attacker, in shots from behind Indy, he's facing one way, but in frontwards shots, he's facing a different way and when it cuts back to behind him, he's facing the other way 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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