Factual error: When the Nazis are meeting with the Sultan of Hatay he remarks he wants their Rolls Royce Phantom II, he quips about the size of the engine being 4.5L engine with 30HP. In reality, the Phantom II had a 7.7L I-6 engine with 40-50HP. Also, the vehicle shown in the movie is a Rolls-Royce 20/25HP Barker Saloon, not a Phantom II. It also makes little sense that the Nazis would be driving a Rolls Royce since it is a British car. In the novel, the car is said to be a Daimler-Benz, which matches what the Nazis actually used in real life.
Continuity mistake: When Indy sees Elsa losing her grip on the tilted earth and then falling on the rising ground during the temple quake sequence towards the end of the film, he lets go of his father, but when the camera changes to behind Elsa in the next shot, Indy is back holding his father again.
Factual error: The stamps on the mail at Sr. Jones house are Texas Statehood issued in 1945. A bit late for the scene. (00:24:15)
Continuity mistake: The tank turret is at a completely different angle when it shoots at Jones when riding his horse.