Factual error: When Indiana Jones is fighting the big German by the airplane, the German punches Indiana Jones on his right cheek. Indy's face and body are both knocked down to the right, in the direction of the punch. When you watch this, you can see it's impossible to be knocked down in such a way. (01:17:55)
Factual error: The film starts in the year 1936, and just like the RPG Indy uses to threaten Belloq with, the MP40s (or at the earliest, MP38s) are an arms-historical anachronism in this movie. As the numbers in their names imply, the MP38 was first produced in 1938. The weapons in the movie are not the similar-looking ERMA MP-36, you can see the ribbed, vertically angled magazine holders typical for the MP40 - its predecessors had either a 30°-canted, smooth magazine holder (MP36) or a round viewing port for checking the ammo (MP38). (01:31:45)
Factual error: Indy's satchel is a Mk VII gas mask bag, which was created for use in World War II, so it didn't even exist at the time the film takes place (1936). The similar Mk V existed at the time, though.
Factual error: It should be a tricky task to put an object the size of the Ark on board a German VIIC submarine; perhaps you can find enough place inside but how do you manage to introduce that bulky case through the narrow hatches of the sub? Even the torpedo load hatches were just a little more than 21 inches in diameter.
Factual error: At the beginning of the movie, when Indiana is looking for the temple, you can hear a bird call. It also can be heard when Indy is running from the natives. The bird is a willow ptarmigan. It lives in very cold areas in the far north of North America. Even a very directionally-challenged ptarmigan could not possibly end up in South America. You can also hear the unmistakable laughing sounds of the kookaburras, only found in Australia.
Factual error: The German submarine that Indy stows away on has the number 26 on its side. The U-26 was a Type IA U-boat (it came into service in 1936 and was sunk in 1940), but the sub in the movie seems to be a Type VIIB or VIIC. It's true that the two types looked fairly similar, but they were different classes of U-boat.
Factual error: The captain of the Bantu Wind, Katanga, wears a hat that originated from the Yugoslav People's Navy. But the Yugoslav Navy wasn't formed until 1945, 9 years after this movie takes place.
Factual error: When Indiana Jones ambushes the Nazis with the Ark, he threatens them with an anti-tank rocket. This is set in 1936, and anti-tank rockets weren't developed until the American M1 in 1942. The Germans immediately copied it from captured weapons and made their own much larger version known as the Panzerschreck, then Panzerfaust. The Russian RPG which Indy is holding was developed from the Panzerfaust in 1949. (00:41:55)
Factual error: The interior of the German U-boat is completely different from the real interior of a Type VII U-boat, which is correctly shown in movies like 'Das Boot' or 'U-571'. For example, the ladder from the conning tower faces a different direction, the map table is too big and on the wrong side, the valves for submerging are on the side of the control room and not at its front and stern, depth gauges are too big...etc. All interiors were standardized, so it could not have been an individual build.
Factual error: When Indy flies to Nepal, there is a scene of the sea plane taking off with the Golden Gate Bridge in the background. The movie is set in 1936, and the bridge wasn't completed until 1937, with pictures from December 1936 showing large gaps still in the deck that do not appear in the movie. (00:23:00)
Factual error: Several times during the movie, Indy is under fire from Nazis or other bad guys wielding what look like MP-38 sub machine guns. The movie is set in 1936, 2 years before the weapon was even designed. The Erma EMP-36 has wooden parts (the grip), the muzzle spike at under the barrel is more pointy and the front sight are more massive than MP-38/40, and the magazine is tilting slightly forwards towards the muzzle. The MP-38/40 is all stamped sheet metal (no wood, because it would slow down production), the muzzle spike under the barrel is more smooth (maybe so it won't get stuck?) and the front sight is more simple (basically just a ring with rumble strips) than the ERMA's, and the magazine on the MP-38/40 is vertical.
Factual error: When Indy is attempting to steal the Ark when driving the truck, one of the soldiers shoots him in the arm. Then another German punches him repeatedly in the same arm, causing Indy great pain and injury. After suffering a wound like that there's no way he'd be able to move that arm, let alone raise it above his head. But the next day after the boat is stopped by the sub, Indy jumps into the water and swims to the sub without any problems.