Continuity mistake: While Henry and Marcus are being held inside the tank, Indiana rides in circles and baits the tank to ram into one of the cars. In a following shot when we see Vogel walking toward the window inside the tank it's a flipped shot, note everything is backwards. Then two shots later, when Vogel shouts "quick" in German it's another flipped shot, and about five shots after that again flipped. (01:29:30)
Visible crew/equipment: After Young Indy locks the two treasure hunters in the reptile train car he pulls a snake out of his shirt, and just as the third young treasure hunter tackles Indy we can see a crewmember's arm and equipment at the left side of the screen, before it cuts to the long shot. (00:07:00)
Revealing mistake: The candles that adorn the wall in the Grail room do not appear to have a strong enough flame to put out the light they do that shines on the wall. In fact, it looks like there are electrical lamps just behind the candle. (01:49:20)
Factual error: When Indy and Marcus fly to Venice, the route map shows them going from New York to Botwood, Newfoundland, then from Botwood to the Azores to the continent. There were two transcontinental air routes at the time across the North Atlantic: one from New Work to Botwood to London, and one from New York to the Azores to the continent, but none from Botwood to the Azores. (http://people.hofstra.edu/geotrans/eng/ch3en/conc3en/earlyairnetworks.html).
Continuity mistake: When Indy is rescuing his father from Brunwald castle, he uses his bullwhip to smash through the window of the room his father is kept in...but in the time it took to jump into the room and get smashed over the head by his father, the bullwhip he used would have lost lots of its momentum and it wouldn't be waiting for him to grab it and use it later on the movie. (00:47:40)
Revealing mistake: When the VW gets stuck on the front of the tank and is shot off, you can see that the car has no engine, no body in the car, and no clutch. Also, when the car is blown away you can see a wire used for the stunt fall right in front of the camera.
Continuity mistake: The back of the boat gets chewed up by the prop in the same place twice.
Factual error: When the soldier from Hatay attempts to pass through the booby trap and his head is chopped off there is no blood. Any wound to the head or neck tends to bleed profusely but the head rolls by without a drop.