Continuity mistake: When the movie beings, the Boy Scouts at the end of the row dismount the horses, then the angle changes and they dismount the horses again.
Revealing mistake: When Marcus Brody is knocked out in the library, he is dragged away by two of the assailants. You can see the unconscious Brody give his right hand to the assailant.
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.
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.
Revealing mistake: In the shot of Elsa falling to her death into the misty chasm in the Temple, you can see that it is not Alison Doody but a stunt double.
Factual error: When Indy and his father rotate into the control room, the eagle on the uniform of the woman who raises the alarm is on the wrong side, left instead of right.
Suggested correction: As it's an SS uniform, the eagle insignia should be on the upper left arm.
Continuity mistake: The blood on Indy's left ear disappears at the end of the film.
Revealing mistake: When Walter Donovan is dying after drinking from the wrong cup, watch the over-the-shoulder shot where we see his hair grow long suddenly - for some reason, this shot was filmed in reverse, as the fire coming from the candles/torches behind Elsa is not burning upwards, but appears to be "sucking" back downwards.
Continuity mistake: When Indy and Elsa come up through the manhole their hair is sopping wet and messy. As they run to the boat their hair is magically styled and not sopping wet anymore.