Continuity mistake: During the palace dinner scene, the "snake surprise" is laid down at Willie's left side. A few shots later it's on her right.
Continuity mistake: While Indy and the Thuggee Chief Guard are battling it out, after the shot of the Maharaja gleefully stabbing the Indy doll, in Willie's next closeup she's wearing the veil as she throws rocks at the Chief Guard, but in the next wideshot the veil is gone, but it's back on her head in following shots.
Continuity mistake: Mola Ram wears a wristband on each wrist and only one armband on his right upper arm, but when he falls off the hanging bridge into the water, in the overhead shot he's suddenly wearing armbands on both upper arms.
Continuity mistake: During the mine cart chase, when Indy grabs the shovel to scrape the underside of the overhead metal bin, Indy's right hand is suddenly missing the cloth which is wrapped around his knuckles in previous and following shots.
Continuity mistake: While the second mine cart with Thuggee goons is in hot pursuit of Indy, note the brake pole at the front of Indy's mine cart keeps vanishing and reappearing in following shots, before it actually breaks off.
Continuity mistake: After Indy's fight with the Chief Guard on the conveyor belt, when Indy attempts to save him from the rock crusher Indy ends up hoisting himself up in mid-air, and when he reaches the platform Indy's shoes are completely flat, unlike Indy's ankle boots which have heels.
Continuity mistake: When Lao Che's goons toss Indy onto the cart at Club Obi Wan, note the soles of Indy's shoes are entirely tan with black heels, but when the cart crashes into the bandstand we see the arches of Indy's soles are black and the heels are tan.
Continuity mistake: After Indy and Willie have jumped out the window at Club Obi Wan, when they land on the lower awnings and roll off we can see Willie's high-heels have become flats.
Continuity mistake: After Indy, Willie, and Short Round jump out of the plane with the raft, when the raft finally slows down in the water Willie falls backwards with her legs up in the air and her high-heels have become flats.
Continuity mistake: Right when Indy cuts the bridge and it dangles loose towards the rocky wall, notice that Willie is above Shorty, both in an X position (very likely replaced with dolls). In the close-up of the real actors, both are very close parallel to each other.
Continuity mistake: After Willie crosses the bridge, right when Indy threatens to drop the bag, her hair style changes completely.
Revealing mistake: During the mine chase, after Indy cries to Shorty "Let it go, our only chance!" the wig of the doll replacing Willie flies away. (01:35:59)
Continuity mistake: During the mine race, the cart behind Indy's flips over and is launched far away from the tracks, yet a frame later it's laying down right on the track for a second cart to crash against it.
Continuity mistake: The beginning of the bridge scene is really chaotic: Short walks several meters ahead, the wide angle shows he's alone, then a frame later he's several meters back plus with Willie next to him, then it cuts to him and again he's alone.
Continuity mistake: While hanging from the bridge, when the Thuggee flies down, Indy is sometimes in a higher or lower place, depending on the shot.
Revealing mistake: When the plane lands against the snowy mountain, no parts fly all over and no snow shatters at all, revealing the composite trick.
Continuity mistake: In the village, the three are surrounded by a huge crowd, yet when Short goes for a walk, half a second later, there's barely a dozen people in front of Indy and Willie. Then it cuts back to the previous wide angle and the huge crowd reappears.
Continuity mistake: When Indy uses his whip to swing into the mine cart that Willie and Shorty are in, the way that he is holding the whip changes from shot to shot. Frontal shots show Indy holding the whip with his hands above his head. In shots from behind, Indy is holding the whip with his hands at his chest.
Continuity mistake: When Mola Ram is trying to get Indy's heart on the hanging bridge, the opening of Indy's shirt keeps changing drastically through shots.
Factual error: After Willie and Shorty step on mola Ram's hands and make him fall off the bridge, a jet airplane is seen on the right side.
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