Revealing mistake: During the mine cart chase, when Short Round's arms are being pulled by the Thuggees while Indy's hanging onto him, in the side wideshot you can see the black safety strap around Shorty's hips, over his pants.
Continuity mistake: When Lao Che's goons toss Indiana onto the dish cart, in the next shot just as Indy notices the rolling vial on the floor and reaches out to it, at the top left of the screen we see broken dishes and broken remnants of the band's podium lying on the floor, but the problem is the goons haven't yet pushed Indy's cart into the podium, which happens three shots later.
Continuity mistake: During the mine cart scene, right after Indy strikes the overhead metal bin, the next wideshot of the Thuggee goons is a flipped shot, note the stripe direction on their turbans and their cart's brake has switched sides. Then another shot with a view facing the front of Indy's cart looking back towards the Thuggee cart, note the brake at the front of Indy's cart has switched sides.
Continuity mistake: After the pilots have jumped from the plane Willie shows Indy the empty cockpit, and in the shot of the front windshield note the view outside and the gauges, then after Indy nervously repeats "fuel" a few times there's another shot of the front windshield which is a flipped shot.
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: 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.
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 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.
Factual error: Neither Willie nor the human sacrifice victim show signs of significant perspiration when being lowered to the lava. They should have been sweating profusely after being close to the lava.
Factual error: Indy rescues Willie from the lava pit and immediately releases her from the cage. In reality the cage would be too hot to touch for several minutes after being that close to the lava.
Revealing mistake: To escape the Obi Wan Nightclub, Indy and Willie jump out the window and fall through several awnings. When they hit the second to last awning, there is a close up on the actors. Just before they hit the awning, there are butt-shaped indents in the fabric from a previous take.
Factual error: The village Indy floats into, supposedly in north India, is populated with people who speak with Indy in Sinhalese, the national language of Sri Lanka. The film was shot on location in Sri Lanka.
Plot hole: In Raiders of the Lost Ark, Indy tells Marcus he doesn't believe in magic or superstition. However, in this movie, which is set a year before Raiders, Indy not only witnesses supernatural acts, but takes advantage of them to win the day (by using the incantation to ignite the stones at the end). Therefore, by Raiders Indy would not only believe in magic and superstition but would know they exist. Listed for this movie as it was made after Raiders.
Continuity mistake: When Indiana, Short Round, and Willie are watching the ceremony at the Temple of Doom, just after Indy says "nobody has seen this for 100 years" you can also see Indy, shirtless, down near the alter on the top left of the screen and the skull is lit up. When Mola Ram walks out, it isn't.
Suggested correction: Just because Indy saw magic and supernatural powers in India doesn't mean he should believe the stories revolving around the ark of the covenant. Stories can still just be stories and not believed even by witnesses of unexplained phenomena.
lionhead
Suggested correction: Indy saw some very surreal things and understands why people would form cultures and superstitions around them, but that doesn't mean he's concluded that it's necessarily "magic" or extrapolated that into a belief in superstition in general. You can read the end of Raiders, in which Indy suddenly orders Marion to shut her eyes when the Ark is opened, as being informed by the events in Temple of Doom and him knowing it's better to be safe than sorry regarding matters like this.
TonyPH