
Continuity mistake: On the boat, when the kid hands Helena the dial, she touches it with her right hand. A shot later, her right hand is away and her left arm is leaning towards the dial.
Continuity mistake: When Indy drives the Nazi car, he turns the steering wheel to our right, but the car skids to the left. (00:07:10)
Continuity mistake: In the tuktuk, Indy tries to snatch the bag from Voller, who grabs it strongly. His left hand changes positions depending on the shot.
Continuity mistake: Indy asks the students if they've done the reading. A boy and girl in the front row turn their heads to the right and stare at him. Shot changes and they are looking away and repeating all previous movements.
Continuity mistake: Indy's horse gallops past a blue car, and then a white one. Shot changes, and now it's metres behind, riding past the white car again.
Continuity mistake: When the Nazi holds the pocket watch in front of Indy, the length of the chain hanging loose changes between shots.

Continuity mistake: When Indy is shot, he falls with the strap of his satchel running down the side of his body. A shot later, he lies with the strap running across his chest. Then, a shot later, the strap is nowhere to be seen.
Revealing mistake: When Hauke breaks the neck of one of the American soldiers in the plane, it is very obvious that he only rests his hands on the soldier's head without twisting his neck. (01:10:14)
Revealing mistake: During the parade, after the red convertible skids, Indy's horse rears. When it turns around, check Indy's face and you'll notice that it's Harrison Ford's stunt.

Continuity mistake: Indy tries to make a phone call but is abducted by the baddies. There's a close-up of the phone and blood has suddenly appeared all over it.

Factual error: The crown on the logo of the Air Maroc plane is the modern 2013 version, not the one from 1969 when the movie is set.

Continuity mistake: Indy stops Basil from hammering the dial and makes the left side of his jacket open to reveal his shirt. Shot changes, and now the opening has swapped sides.

Continuity mistake: Indy horseback rides past a truck with a flag, then between a dozen of musicians while chased by a motorbike. When he looks behind him, the band has vanished and the truck is next to him again. This last shot belonged in the first place.
Continuity mistake: Gunther exits the van and shoots a mechanic in the airfield, in his full movie costume. However, just a few seconds later, he's fully dressed as an SS Sergeant.

Continuity mistake: When Indy is hanged, the bomb falls downwards slowly. Check the writing on it, and you'll notice that a shot later, the bomb has moved upwards and is repeating the previous movement.
Continuity mistake: When Indy is hanged, the bomb is stuck parallel to the ground. A shot later, it's perpendicular to the ground.
Continuity mistake: While on top of the train, Basil waves one arm, pleading for the train to stop. The shot changes, and he's waving both arms.
Continuity mistake: At the farewell celebration for Indy's retirement, the dean calls for the gift to be presented to him, mentioning it is "a token of our gratitude." There's a cut in the middle of the sentence, and Prof. Plimpton is waving a young student in with his left hand, then the right hand.

Factual error: All of the police cars in New York City are painted in a blue and white livery, but until 1973, NYPD cars were painted black, white, and green.
Answer: There is a bit of dialogue en route to the airport when Voller sets the instrument that says, "the first hand sets the destination," as in the time you want to travel back to. This would make the device completely absurd in principle if true (that's why I wanted to mark it as a plot hole/stupidity). Since it's supposed not to open portals but just detect them, it can't be that there are infinite portals for every moment in time you can choose to go back to (and they even close). The sky, while vast, is not infinite. We then find out that it is a trick since it is set to actually bring you to just one destination, but they don't know it yet.
Sammo ★