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.
Continuity mistake: After pilots jump from the plane, there is a shot showing a view from the cockpit. You can see a propeller standing still, even before the fuel runs out. (00:16:00)
Continuity mistake: When the girl falls off the elephant, she falls off head first, and during a 5 foot fall, at most, manages to do a complete flip and land on her backside. (00:31:00)
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.
Audio problem: When the group piles into the lifeboat on the crashing plane, Shorty (who is stuck between Indy and Willie) exclaims "Indy, I can't breathe!", but his lips don't move. (00:17:35)
Continuity mistake: As Willie Scott frantically searches for the diamond after the ice has been spilled on the floor, the red glove on her right hand disappears. (00:09:35)
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.
Continuity mistake: Some bad guys throw knives at Indy as the band is seated and playing "Anything Goes". Then Indy throws a cymbal at one of the bad guys and the entire band is now gone. (00:09:30)
Revealing mistake: At the end, the elephant that the kid is riding sprays Indiana and Willie with water. If you watch very carefully, Harrison winces in anticipation right before the water hits them. (01:52:30)
Continuity mistake: As Indy, Willie, and Short Round are going down the river in the raft, their positions in the raft keep changing, from Indy being on one side of them, to being in the middle, then on the other side, etc. (00:18:25)
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 Indy is fighting on the conveyor belt, he is about to be run over a couple of times, but in the next shot he is further away. (01:31:40)
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.
Continuity mistake: At Club Obi Wan, Indy reminds Lao Che that Kao Kan tried to get Nurhachi without payment, and when Kao Kan raises his hand we see the gauze wrapped around his palm with a strip from his thumb area going diagonally down to his wrist, but in the next shot the gauze strip is wrapped diagonally from the opposite direction.
Continuity mistake: After Short Round snaps Indy out of his trance, when the Thuggee continues to lower Willie we see in her closeup that the flowers in her hair and the flower garland around her neck are already shriveled and blackened, but in her next closeup the flowers are back to being vibrant and fresh.
Continuity mistake: After Willie's rescue, when she tells Indiana they should get out of there, in the next closeup just as Indy says, "Right, all of us," this is a flipped shot, note Indy's Fedora, chin scar and red strap.
Revealing mistake: During the mine cart scene, after Indy notices that the track cuts out, just as the mine cart flies over the expanse there's a vertical wire at the back of the cart, leading up to the top of the screen, and a horizontal wire at the front of the cart, leading toward the right side of the screen. Additionally, when the mine cart lands on the other track keep your eye on the top edge of the screen as something dips into view, but it's pulled back up immediately, right before the shot cuts away to Mola Ram. The wires and the mysterious object can be seen when viewed on Amazon Prime, but they seem to have been edited out of the DVD (2008 version) I own.
Revealing mistake: When the second band of Thuggees are in the mine cart pursuing Indy's cart, note the metal bar attached to the back of Indy's mine cart which wasn't there before, for use during the ensuing stunt. That bar then disappears and reappears.
Continuity mistake: At Club Obi Wan, Indy places Nurhachi on the table in the closeup with his left hand, but when Indy puts the diamond on the table with his left hand it's not actually Indy's hand that we see in this shot.
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