Other mistake: One of the soldiers at the table Sallah and Indy walk next to, is only pretending to eat with his spoon. (00:54:53)
Continuity mistake: In the chapel, before Indy turns the chalkboard over to explain the staff of Ra and the medallion to the G-men, the chalkboard goes back and forth from tilting forward to tilting backward a few times.
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.
BaconIsMyBFF