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 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: 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 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.
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)
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)
Trivia: Not a mistake, just something that's not immediately obvious: When they arrive at the plane after the club scene, the man that walks them to the plane is Dan Aykroyd.
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)
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.
Continuity mistake: During the melee at Club Obi Wan, Lao Che's goons toss Indy onto the dish cart which has a horizontal metal bar between two of its legs over the wheels, but in the closeup as Indy tries to grab the antidote vial, the metal bar has vanished, but it reappears when it crashes into the bandstand.
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.
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: When the pilots jump from the airplane we see Willie asleep directly under the rolled up tapestries, but when she wakes up and starts to make her way to the cockpit as she coughs, in the wide shot we see she's coming from the area that's further in the back toward the tail.
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.
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: After Willie saves Short from the hole in the bridge, the river is filled with water. Seconds later, when Indy is about to cut the bridge, there's a wide angle where there's barely any water, with rocks coming out. Then he cuts the bridge and it's filled with water again.
Answer: This is conjecture, but it seems the general function of setting Temple of Doom before Raiders of the Lost Ark is that it helps set audience expectations that the two movies are self-contained episodes. For instance, Karen Allen has said she wasn't disappointed about not being asked to return because she'd already been told that the next installment was being set in the past before her character is reunited with Indy. Conversely, since we're already aware Raiders makes no mention of the events of Temple of Doom, we know we shouldn't necessarily expect any further installments to continue directly from prior movies' storylines regardless if they are set forward in time.
TonyPH