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).
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.
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.
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.
Factual error: In the 'The Last Crusade', the Germans and their lackeys use MP 38 or MP 40 submachine guns extensively. The MP 38 was still a new weapon in 1938, and not around in such large numbers to arm each and every soldier with it (total of 1 million MP38/40's vs. more than 20 million troopers in WW2).