Factual error: When they fly from Shanghai (southern China) to India (southwest of China) you see the plane passing the Great Chinese Wall. But the wall is placed in northern China, not on the route Shanghai - Chungking - India. (00:14:35)
Plot hole: Mola Ram has his men knock over a vat of water in a last ditch effort to kill our heroes. First of all the vat can't be that big if it can be knocked down with a few sledgehammers. Secondly, for the amount of water that chases Indy and co. down the vat would have to be big enough to fill the room it's in, which obviously it's not. Third, Indy and co. travel through several large caverns during the mine cart chase, caverns that could easily swallow up any of the water flowing through the tunnels so there shouldn't be any water left to catch up to Indy by the time they stop.
Continuity mistake: Outside the club, a sailor and a girl are in a buggy, which crashes. When the buggy is on the road, the sailor is on one side - when it crashes, he is on the other side, having swapped places with the girl. Some shots are flipped, note the car's license plate. (00:12:05)
Revealing mistake: During the chase with the carts in the mine, in some of the shots, you can see that figures who are supposed to be Indy, Willie and Short Round are dummies. Indy's arm especially belongs to a mannequin in the shot where the cart almost derails. (01:36:00)
Continuity mistake: All during the fight in the sacrifice temple, the strap across Indy's chest hangs from his left shoulder to his right side. When he hugs Shorty, the strap is reversed. Also, the blood on his mouth occasionally switches sides, as does the parting of his hair. They obviously flipped the negative. Fixed in some DVD versions.
Revealing mistake: When Indy and Willie jump out of the Obi Wan Nightclub, they fall through several awnings, the idea being that they will break the characters' fall. All well and good. But, if you look very carefully, you can see small taped-up cut marks which the crew made so the stunt men (and women) could effortlessly glide though the awnings.
Continuity mistake: When Indy, Shorty and Willie are looking at the ritual from the "balcony" in the cave, they take a look at the big skull on the wall. The artifact stones aren't placed in the skull. In the next shot the stones are there. After a few seconds the camera turns and the stones aren't there again. Some minutes later some of the bad guys bring them and put them in the skull.
Continuity mistake: During the mine cart chase, in the first wideshot of Shorty being pulled between the two carts where we see the lava under Shorty, this is a flipped shot. Note Indy's ripped sleeve is at his left side instead of his right, and the stripe on the Thuggee's turban is the opposite direction than it should be.
Continuity mistake: When Indy is at the banquet, he has a large silver platter in front of him with a smaller plate of food on top of it. When the maharajah speaks, his smaller plate of food has mysteriously disappeared.
Continuity mistake: The scene in the Obi Wan nightclub when Indiana runs out of the window with Willie Scott. Indiana is running behind the gong and we see him collect Willie. In the next shot seen from behind the gong Indiana has yet to reach Willie before they jump out of the window.
Visible crew/equipment: When Indy enters the dungeon, he is using a match to lighten the writing on the wall. You can see the shadow of his whole arm which shouldn't be visible if that match was the light source. (00:53:15)
Continuity mistake: When Short Round is dangling between the two carts, just before the cart tracks split, he goes from being held by one arm to suddenly being held by two. (01:33:25)
Continuity mistake: During the escape from the mine, Indy has to slide along on a rope to catch his companion's cart. Whilst hanging from the rope the shot switches from in front to behind a number of times. Depending on the shot, Indy switches from barely hanging on to having the rope grasped tightly next to him. (01:34:45)
Continuity mistake: When Indy and Willie are waiting for each other to come to their respective rooms, Indy's clock shows the time as 10.17 and yet when the Thuggee guard tries to strangle Indy, the same clock shows the time at 10.36. (00:50:10)
Continuity mistake: Willie Scott's fingernails are considerably shorter in the nightclub scene compared to when she "burns her finger and cracks a nail" in the car. (00:04:45 - 00:12:35)
Continuity mistake: When Indy is struggling on the bridge, he breaks one or two of the planks. When they are shown again, they are undamaged.
Continuity mistake: When Indy starts climbing up the cliff after the water bursts through, we see a close-up of the back of his shirt, and there's one small tear quite high up. We cut to a wide shot, and now there are several quite wide rips across the back of his shirt. (01:36:30)
Visible crew/equipment: When Indy appears at the entrance of the mining caves to free the enslaved children, he punches out one of the guards and he goes flying in the air and across the gravel. You can see two suspension wires attached to the actor to drag him back through the dirt. (01:27:45)
Continuity mistake: When Indy is in Club Obi-Wan, he spills a drink down his front. In the next shot, he is completely dry.
Factual error: The British / Indian troops at the end of the movie are using Lee Enfield no4Mk1 rifles. These didn't go into production until 1940. Also India never used the no4Mk1, they used the no1Mk3 until the 1950s.
Chosen answer: His neck was snapped by the whip getting caught in the fan. There isn't always blood with a hanging. Since the fan wasn't designed to hold a man's weight, the motor in it would have stopped or given out.
Captain Defenestrator