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.
Continuity mistake: When Helena is doing the magic tricks, Renaldo reaches for the cards with both hands. Shot changes, and he is reaching just with one.
Continuity mistake: Before the tuk tuk comes to a stop, a man in a blue djellabah is walking by next to it. When the tuk tuk stops, the man is suddenly 3 meters behind, repeating all previous movements.
Continuity mistake: Before Indy jumps on the horse during the parade, a man in a plaid shirt runs away. Shot changes, and he is back in the previous position, yet he is now walking slightly faster.
Continuity mistake: When the staff member at the college runs away from the bad guys to get help, and is quickly shot in the back by Voller's henchman, she falls forward on the floor, face down. Dead. But a short time later, when Indy discovers her body on the floor, he kneels down to attend to her (and looks at his hand to see her blood there), she is now lying face-up on her back.
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 the guard of the airfield's gate, in his full movie costume. However, just a few seconds later, he's fully dressed as a SS Sergeant.
Continuity mistake: During the tuk tuk chase, skid marks from previous takes are visible on the road. (01:03:13)
Revealing mistake: When Helena locks up Indy in the upper level of the archive room, there are two angles shot from the ground floor when the baddies shoot at Indy and he dodges the bullets. One can blatantly see that's not Harrison Ford but a guy with an ugly mask on (many scenes were performed by stunts wearing latex masks, as the making-of videos show).
Plot hole: At the start of the film, a young Jürgen Voller gets hit square in the face, at high speed, by trackside equipment and gets knocked off the train. But somehow, he isn't killed and survives without so much as a scar on his face.
Continuity mistake: When the villains are following Indy through the caves, the old wooden bridge completely breaks and falls apart. However, when they make their escape across the same bridge, it's intact with only a couple of wooden slats broken.
Factual error: The four-barrelled Flak gun is shown running out of ammunition, namely a belt of rounds. This is most likely intended to be a Flak 38, which used twenty-round magazines, not belts. It had a relatively low rate of fire as the magazines had to be constantly swapped out, and two barrels were usually fired at a time. (00:16:58)
Factual error: When flying towards the time fissure, the German commander says that Hitler is awaiting info on the V-1 project. They're supposed to be heading for a date shortly before Germany invaded Poland. The V-1 project started in early 1942, and it wasn't named the "V-1" until June 1944.
Factual error: Basil Shaw is British, but the dates in his notes about the Antikythera are all written in American format (MM-DD-YY), as opposed to DD-MM-YY.
Other mistake: As the divers prepare to descend to the Roman shipwreck, none of their buoyancy aid inflation valves are connected to an air intake. This makes the rapid inflation, which happens on their ascent back to the surface, impossible. (01:15:15 - 01:15:50)
Factual error: The night before Indy dives on the Roman wreck, his co-star describes the plan. An initial 70ft drop, followed by a further 300ft descent to the sea floor. Essentially, if you breathe compressed air to equalise your lungs to the surrounding pressure, then you cannot ascend to the surface rapidly from that depth. Breathing normal air, you can suffer from oxygen toxicity at around 56m. Due to the partial pressure law, at 370ft/112m, you would need a heliox mix (10% oxygen) from a second tank to survive. (01:21:00 - 01:22:08)
