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.
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.
Other mistake: In Tangiers, Indy's cab pulls over in front of the mob-owned hotel where the famous illegal auction is taking place. It's dark outside, but when we see Indy in the hotel, and more evidently when they get out of the hotel and the car chase starts in the span of 5 minutes, it's broad daylight. That also means that just before 6 AM (when dawn would take place in August), the hotel is chock full of normal people boozing, playing cards, plus an assembly of rich baddies from all over the world who just happen to wait to have an auction.
Continuity mistake: When Teddy is abducted, Indy runs towards the car, past a hat lying on the street. The shot changes, and he is metres behind, running towards the hat again.