When Short Round and Indiana Jones walk over the floor of bugs, Short Round refers to the crunching as "Walking on Fortune Cookies". Prior to WWII, fortune cookies were called fortune tea cakes, and largely only served in America.
In the overview shot in the mine, just before Short Round and Dr. Jones end up in a metal cage and learn about Kali's Blood, one of the men sending sparks in the air in the middle of the screen is sporting a very obvious blue/metal disc cutter.
When the British Indian Army Riflemen arrive and fire on the Thugees, they are firing Lee-Enfield No. 4 MkI Rifle although the film is set in 1935. The No.4 Mk I was not first issued to British troops in 1939 but was not adopted officially until 1941.
The Tri-Motor instrument panel shows two flight navigation instruments that would not have existed at the time of the film. One was an RMI or radio-magnetic indicator the other was a VOR OBI or omni-bearing-indicator. Both use radio beacons that were not in use until the '50s.
When Indiana Jones and Short Round were caught in the room with the ceiling coming down at Pankot Palace, spikes come out of the ceiling and we see a wide shot of Indiana Jones and Short Round in the corner of the room. In the very next close-up, Indiana yells, "This is serious!" But in the wide shot, his mouth moves, mouthing, "This is s - !" but no audio is heard. He also slightly slouches while saying the line, the way he does in the closeup. All this indicates that the footage of Indiana Jones yelling, "This is serious!" was used twice... for some strange reason.
When Indy and Shorty exit the Village Elder's hut, Shorty asks if they made the plane crash to get him there. Indy replies, "No Shorty, it's just a ghost story, don't worry about it," but his lip movement does not match the speech.
Although they might be consumed in some parts of Southeast Asia, snakes, insects, and monkey brains would never be served in India (and especially not in the palace of a Hindu king or "maharaja") due to very strict Hindu and Islamic dietary codes. In fact, a significant portion of Indians (mostly Hindus) are strict vegetarians due to those religious dietary restrictions.
In the Indian village, in addition to everyone speaking Sinhala - the Sri Lankan language - the old man speaks English in a Sri Lankan accent, implying he is a Sri Lankan, not an Indian and that the scenes were probably shot in Sri Lanka using local actors.
When Indy flees from the gang of Thugees after the swordfight, he is dragging his whip behind him. Yet in the next shot when he reaches the bridge, it is rolled up neatly even though he doesn't have a free hand or time to roll it up.
During the climactic fight scene when Short Round tackles the Maharajah, the Indy doll and the hairpin clearly separate as the young prince falls to the ground - the pin, with its feathery handle, remains in his right hand and the doll in his left. Yet, when the Indy doll is next shown lying on the ground, the hairpin is still stuck into it.
After falling from the airplane, while rafting down the river in the yellow inflatable boat, during each of the closeups, Indiana Jones is on Willie's right, but in some of the long shots, their positions are reversed.
During the battle in the temple, Mola Ram removes his helmet, but as Indiana lunges towards him with a club, Mola Ram is seen with his helmet on. In the following shot, before disappearing through a trap door, the helmet is off again.
During the sequence where Indy and Short Round rescue Willie from the sacrificial pit, Chattar Lal's body disappears from its position next to the winch, once Willie has been released from the cage (a sequence was storyboarded, but not ultimately filmed, where Lal was thrown into the pit, which explains why his body wasn't originally intended to be in the shot).
Willie's position relative to the rolling gong changes suddenly during the quick scene. The gong first passes in front of her; cut to behind the gong and she is well in front of it; then after a shot of the gunman, Jones grabs her behind the gong.
After the pilots jump from the Ford Tri-motor 4AT, Willie looks through the curtain into the cockpit. The next scene is her view out the cockpit window and the nose engine is clearly stopped with the stationary prop clearly visible at the 1:00 position before they start running out of fuel. After Indie starts checking the instruments another shot through the windscreen shows the nose prop at the 11:00 position. In yet another shot as the airplane clips a mountain ridge, the nose prop is back at 1:00 again.
After the Chinese pilots jump from the Ford Tri-motor 4AT, Indy and Willie watch the propellers shut down as the plane runs out of fuel. When the plane brushes the mountaintop, the non-operational props are clearly visible. Yet when Indy, Willie, and Shorty bail from the plane in the emergency raft, we can see that all three props are fully operational.
When Indiana is hanging from the bridge holding one half of his bag and the other guy is holding the other half the bag catches on fire as the stones fall. After Mola Ram falls and Indy climbs up, the front of his bag is intact. When they are walking to the village after that he is wearing the bag behind him with clearly no burn marks. Then in the next scene it disappears and reappears.
When Indy is fighting after being awoken by the fire, he is attacked by a man with a spear who is pole-vaulted into the lava. In one shot you can see the V for the pole in the next shot it is gone then comes back.
As Indy dodges the weapons thrown at him by Laos' men in the club, you can see the band right next to him, still playing. However, a second later when he throws the cymbal at one of the men (the one who knocks over the ice), the band has disappeared.
During the fight scene at Club Obi Wan, Willie is wearing a red glove on her right hand as she looks at the ice cubes spilled on the floor. A second later, as she searches for the diamond among the ice cubes, the glove is gone.
When Indiana, Short Round, and the girl are riding to the palace on the elephants they all start out on their own elephant. In the next shot where Indiana tells Lily they are going to the palace, Short Round is on Indy's elephant and his elephant is tied behind Lily's. In the very next shot where Lily is blown off the elephant, Short Round is back on his own elephant.
After Indiana is burned by the torch and returns to his normal self, he goes to attack Mola Ram. The camera cuts to Mola Ram and he is standing there with a grin on his face. Immediately in the next scene when Indiana steps forward to attack him, he is lying down on the ground and disappears through a trap door.
The Thugees place three Sankara stones in the center skull during the ceremony and one of the stones has three lines across it, which is placed in the nose of the skull. Then when Indy removes the stone from the right eye hole of the skull, which is the one with the lines. Only one of those three stones has lines across it.
When Short Round jumps up and down on the rope bridge, several bridge slats break off causing Shorty to nearly fall through, but when Willie rushes over to help him back up, we see only one slat broken off. Consequently in a later shot, Indy runs across the bridge and the broken slat has been mysteriously repaired.
In the scene where Indy, Shorty and Willie leave the village by elephant we can see Shorty sit on a small elephant. However in one of the next shots we can see Shorty sit in front of Indy on his elephant. In the next scene Shorty is back on his own small elephant.
When the natives take their elephants and leave Indiana, Willie, and Short Round behind, they have no baggage. Yet when Indiana attends the dinner that evening he sports a nice-fitting coat and trousers, and a bow tie, apparel that would hardly be available to be loaned to him in a palace in the middle of India.
As the main characters begin their journey to Pankot Palace, they all get on their own Elephants. In the following scene when Willie pours perfume onto hers, suddenly Short Round is riding with Indy. In the following scene when Willie's elephant hits her with water, Short Round is once again on his own elephant.
When the monkey brains are being placed on the table. The position the monkey heads are "looking" constantly changes direction. They are always "looking" into the camera, no matter where the camera angle cuts to. Sometimes even in opposite directions.
During the scene when the water blasts out of the mine, Willie is seen barefoot almost falling off the of the cliff. However, in the following scene, after Indy cuts the bridge, Willie is seen wearing flip-flops.
When Indy is attacked by the guard in his room, he leaves his whip behind after killing the guard. He never returns to his room and Indy has his whip with him when he swings down into the temple of doom.
When Indy and the group first reach Pankot palace and speak with the Prime Minister, Willie is barefoot. Immediately afterwards, the group enters the palace for the first time and Willie is shown wearing shoes.
As Indy is letting the slaves loose using the keys, there's a shot of all the kids running out of the temple. Short round is among the kids, but in the next scene we see Shorty with Willie watching as Indy is being beat up by one of the main Thuggee guards.
Lao barks at Willie to "Sit Down!" after she complains about the two holes Indy has made in her dress. In the wide shot of Willie sliding onto her seat, you can see a crew member's head lift very briefly to the right of her chair, as he is obviously helping Kate Capshaw shift the chair across the floor as she sits.
In the beginning Lao Che's freight plane is seen flying over the Great Wall of China. Then there is a map with a straight line from Shanghai to Chungking. The wall is no where near that but further north and west of Shanghai closer to Mongolia.
After Indy takes off from Shanghai in the Ford Tri-Motor 4AT, we see a shot of the plane flying over the Great Wall of China just before the map comes on screen, but then the map shows the plane's route as going from Shanghai, WSW to Chungking, and again West onto India (before crashing). The Great Wall of China snakes across Northern China north of Beijing, which is hundreds of miles north of Shanghai, so the plane's route, according to the map, takes it nowhere even close the Great Wall.
When the Chinese pilot activates the fuel dump, we can see a gauge in the cockpit with the front shape of a bimotor plane, and 3 red lights to show if the undercarriage is up or down. The Ford Tri-Motor is not tricycle, as shown in the gauge, but a taildragger. Also, her undercarriage is fixed, not retractable.
The Ford Trimotor of 1935 had no automatic pilot and had to be hand-flown (someone steering the plane) at all times. When the Chinese pilots left the control wheels in the cockpit, the plane was at the mercy of aerodynamics and the elements. Flying over mountains where there would be updrafts and downdrafts would have immediately upset what little equilibrium the plane would have had and immediately put it into and bank and/or dive instead of flying straight and level as it did in the movie.
Indy points to some bats and says that they're vampire bats. Although true vampire bats are indigenous to South America, the bats he is pointing at are Large Flying Foxes, binomially called Pteropus Vampyrus. So given their size it is not unthinkable to refer to them as "Giant Vampire Bats" Also he was trying to frighten Willie.
The altimeter in the plane's cockpit is controlled by someone turning the pressure setting knob. This is clearly visible after the engines run out of fuel and the plane starts to descend. The closeup of the altimeter shows the pressure indicator spin with the hand of the altimeter, although it should remain still as the hand is normally moved by the change in the outside atmospheric pressure only.
When Willie is in the room with the bugs, it is very obvious that she is holding her thumb under her hand to hold in the stick bug as she turns her hand over. With this being a real bug for the scene, they were not able to stick it to her hand or anything like that.
Throughout the length of the mine cart chase, Indy and friends pass through many wide-open chasms as well as several forks on the track, but yet the rushing water at the end of the chase somehow manages to traverse through all of those and still make it in full force to Indy and friends at the end of the track.
When Indy is fighting the man in his room, the man gets the whip around his neck and caught in the fan. The fan pulls him up as far as he can go but in the next shot he is still being pulled up. then in the next shot he is hanging a good 3 feet below the fan.
The amount of water that spilled out of the overturned water tower would not make it all the way to the end of the tunnels where Indy, Willie, and Short Round escape to. There were several instances where the rail car tracks went over large chasms of molten rock in which the water would have evaporated or filled up before it ever reached the end of the tunnels.
The goof items below may give away important plot points.
Indy manages to get the Shankara stones to turn red hot by uttering the incantation, "Tum Shiva ke vishwaas-ghati ho!", which is Hindi for, "You are a betrayer of Shiva." Considering that the stones are supposed to be ancient, any incantation that would make them do anything should be in Sanskrit, the ancient language of India, not Hindi, a language that reached its modern form in the late 18th and early 19th centuries.
The lava is unique. Initially when Willie, Indy and Short Round witness the first sacrifice, the metal cage is brought up again after being dipped in the lava, and is not melted, warped, or affected by the intense heat in any way. Later, when Willie is held over the lava, she is unaffected by the heat, when realistically just being that close to the lava would have severely burned her and probably killed her. When she's raised from the pit, the cage is cool enough to handle, when it should have burned their hands. With real lava, they would only have to be held over it to burn them; dipping them in would have melted the cage.