Factual error: The truck that turns over and blows up after Indy shoots the driver is a Mercedes Benz L701. It began production in 1944, and this movie is set in 1936, so the truck is not period correct. Also, the alleys are too narrow to allow this truck to turn a corner.
Continuity mistake: At the beginning of the film, When Indy uses the whip to take the guides gun away, Satipo makes a weird face and starts to move away in amazement. The very next frame, in a wider shot, he is not finishing his movements, but on the contrary he is standing still, with a normal gesture, until a second later he starts to repeat the movement and looks from before.
Revealing mistake: When Belloq's head explodes, the actor has been visibly replaced by a dummy.
Continuity mistake: After Satipo runs with the idol, Indy grabs a root to help him climb up the ledge. Half a second later, from a different angle, the root is meters away and he is grabbing it again, repeating the whole scene.
Continuity mistake: Just before the car carrying Marion in the wicker basket explodes in the alley, Indiana shoots a man twice in the chest. The man has blood stains on his shirt before he is shot.
Continuity mistake: As Indy and Marion are starting to run from the plane, you can see the yellow wheel chocks are back in place under the plane's tires.
Continuity mistake: After Indy steals the idol, while he is hanging in the well, in the front angle his left leg is bent and already outside, in a quite comfortable and secure position; yet in the angles from behind both legs are inside, hanging loose.
Continuity mistake: After hitting one thug, Indy jumps out of the way of one trying to spear him, leading to the one behind Indy getting run through. As the guy gets run through, he is in front of a hanging string of fruit, with the stacked fruit to his right. After a cut scene to Indy and Marion running away, the run through thug is now facing the fruit stand, setting up the sight gag of the blade sticking out with two fruits stuck on it.
Continuity mistake: While Indy is in the Well of Souls, Belloq greets him and is standing by one of the four sides of the rectangular hole. A frame later he stands by one of the corners.
Continuity mistake: After grabbing the idol, the cave starts to collapse, filling the place with rocks and rubble. When Indy starts to run, from the angle behind the floor is clean, rocks starting to fall for the first time.
Continuity mistake: Satipo drops the whip half a meter away from the closing gate, then runs away. However, when Indy rolls underneath the door, the whip is laying right next to it.
Continuity mistake: When Indiana is hiding his face with the cloth, watch as he enters the tent that Marion is being held prisoner in - at first, Indiana has to hold it in place; in the next shot, he has it tucked into the rest of the folds. The next shot, the actual position of the cloth changes.
Revealing mistake: The Pan American aeroplane Indiana Jones boards in San Fransisco looks similar to (but has noticeable differences from) the Boeing 314 PanAm used for transpacific flights. This aeroplane did however not fly until 1938 and at the time of the story the company only flew transpacific with Sikorsky S-42s, an aeroplane with a completely different body than the one used in the scene.
Revealing mistake: When Indy is fighting the big German at the base of the airplane, Indy reaches down and grabs a handful of sand to throw in his face. You can see the finger marks in the sand from a previous take.
Audio problem: When Marion meets up with Indy on the steps of the building at the very end of the film, she asks what was going on in there. Her first few lines of dialogue were dubbed in after shooting. Her mouth isn't moving with the dialogue.
Factual error: Several times during the movie, Indy is under fire from Nazis or other bad guys wielding what look like MP-38 sub machine guns. The movie is set in 1936, 2 years before the weapon was even designed. The Erma EMP-36 has wooden parts (the grip), the muzzle spike at under the barrel is more pointy and the front sight are more massive than MP-38/40, and the magazine is tilting slightly forwards towards the muzzle. The MP-38/40 is all stamped sheet metal (no wood, because it would slow down production), the muzzle spike under the barrel is more smooth (maybe so it won't get stuck?) and the front sight is more simple (basically just a ring with rumble strips) than the ERMA's, and the magazine on the MP-38/40 is vertical.
Continuity mistake: After Indy replaces the idol for a bag filled with sand, the position of the bag changes between frames.
Other mistake: During the truck scene, after the German soldier hanging onto the door falls down and another guy crawls over the roof, palm trees are reflected on the windshield, but wide shots show not a single tree around because the palm trees area was left behind a while ago.
Continuity mistake: In the map room, after Indy has discovered where to put the stick in, the sun rays lights the head and shoulder of a painted figure and the whole body of the figure to the right of it. A frame later the first figure is now completely lit. Too fast a change.
Continuity mistake: When Belloq talks to Indy in the Well of Souls the two Arabs on the left disappear in the angles from Indy's POV.
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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