Continuity mistake: When Indy climbs onto the circus train, he begins to be chased by Half Breed and Fedora. However, in the next shot, when Indy enters the reptile car, it is now Rough Rider who is behind Half Breed. (00:06:22)
Other mistake: After getting on aboard the dirigible, Henry is holding a German newspaper when addressing Indy. But he'd have a hard time reading it as it's upside down. Even if he's just trying to hide, holding an upside-down newspaper would draw the attention of suspicious guards.
Suggested correction: Henry Jones Sr. doesn't have his glasses in this scene. He can't really see anything on the newspaper, that's why he is holding it upside down.
I'd say that, more than anything, a hasty attempt to blend in would be more likely the culprit. Even without the spectacles, Henry, being the fastidious person he is, would have righted the paper, with or without eyewear.
But since he couldn't see the letters, how would he have righted the newspaper (or even noticed it was upside down)?
Ipon! (Japanese for "point.") I can see your point; however, I would ask that the following be considered: that there is usually more than just letters and words in newsprint. Even if not viewed, pictures are good indicators of the newspaper's orientation.
Continuity mistake: Henry pulls up Indy with both arms, but when the shot changes he is pulling him up with one arm only.
Continuity mistake: When Indy is in the cliff reaching for the grail, his hand swaps between clean, dusty and sweaty, between shots.
Continuity mistake: Henry tells Indy "let it go" and Indy takes his left arm to where his father is. Half a second later his arm is away and he repeats the previous movement.
Continuity mistake: When the grail falls down the cliff and Elsa and Indy try to grab it, the ground it lies on is either yellow or brown. This changes back and forth and has nothing to do with lighting.
Visible crew/equipment: At the beach, right before Dr. Jones scares the birds there's a zoom-in close-up of his face and a crew member approaching is reflected on his glasses.
Revealing mistake: The seagulls on the beach (when Dr. Jones scares them with his umbrella) are blatantly fake. They don't move an inch. This was also confirmed by producer Robert Watts in this making-of video https://www.youtube.com/watch?v=BMFMKsrXuGY (minute 2'30").
Other mistake: In the fighter plane scene, their hats don't blow away.
Continuity mistake: While being chased by the plane, Dr. Jones faces backwards and cries "This is intolerable!", then faces forward and ducks. From the immediate wide angle he is still facing backwards.
Continuity mistake: During the escape from the Nazis the Jones boys pass through a boathouse and Indy sets a small boat loose with the engine running to distract them. When he releases the boat the motor (and boat) is turning to the starboard side (which would turn the boat straight back into the bank), but when the Nazis arrive, the boat is running perfectly straight down the river.
Continuity mistake: When Indy and his father take the car from the old man, you can see that viewed from behind Henry is the driver and Indy is next to him. In the next shot, they have changed positions and Indy is now driving the car.
Audio problem: Just after young Indy escapes the bandits on the train, he finds the magic cart and says "Magic" to himself, but a close look will show his mouth doesn't move with the line.
Continuity mistake: After Indy and Elsa exit the catacombs through a sewer and start to run away, a woman in pink turns her head to watch them leave and then turns around to see Kazim's men run after the couple. A frame later, from a new angle, the woman's head is turned 45° facing downwards.
Continuity mistake: Sallah rescues Dr. Jones from the tank and stops by the cliff. On the next wide angle he's nowhere around.
Continuity mistake: Indy stops his sidecar at a crossroad, meters ahead of a house. When the angle changes he is now several meters behind.
Continuity mistake: During the crashes by the border control the road keeps swapping from sunny to shadowy back and forth in less than 3 seconds.
Continuity mistake: When Marcus watches the carbon copy of the shield, his ice-bag is on the table, but when the angle changes he has it next to his head and seconds later he puts it on the table. Also, the ashtray moves backwards between shots.
Continuity mistake: On the tank, Indy is punched and the gun falls inside. His hat also falls off, but a shot later it's back on, perfectly tucked in.
Audio problem: When the temple floor cracks, Indy holds Elsa from falling into the void and she gives a very loud cry, but her mouth is closed.
