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.
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.
Continuity mistake: The dancers pick up some red handkerchiefs creating a narrow tunnel for Willie to walk through. A frame later they are spread 15 meters apart and just two dancers are parallel to each other holding the fabric.
Visible crew/equipment: When Indy is on the rope bridge at the end, his sword keeps reflecting the white lights being used to illuminate the scene. The sun wouldn't be at the angle he's reflecting as it would be up in the sky, not behind the camera where this light source is.
Other mistake: When the airplane Indy and company are flying in runs out of gas, there is a close up of the instrument panel. The hands of the altimeter start spinning as the plane descends. However, so does the altimeter setting at the side. The altimeter setting is changed by the knob at the bottom. It does not change with altitude.
Revealing mistake: When the water floods the mine, some shots of the 3 heroes are an obvious composite of their blue screened image over a set. Problem is, when Indy tells the two to run towards a tunnel on the right with a log blocking the way, Indy and Shorty run through the log as if they were ghosts.
Continuity mistake: Before Mola Ram hides through a trap door on the floor, his hat is off except for a very brief moment when it's on.
Factual error: They escape from the plane using a life raft and fall a considerable distance (looks like hundreds of feet) before landing on a snowfield. They then slide down the snow and off a cliff before landing in a fast flowing river, again falling a considerable height. There is no way they would be able to fall that distance and land on snow covered ground or a river without being killed or seriously injured, but they are completely unscathed.
Factual error: The self inflating boat on the "South China Air" plane is the typical modern colour yellow and modern shape, which didn't exist at that time.
Revealing mistake: After Indy escapes from the conveyor belt, he runs on some suspended planks while being shot at. Watch the planks: There's black masking tape where the explosives are (which disappear in later shots). Furthermore, right before he takes out his whip, he grabs a railing where the bullet has just hit, and you can see that the black tape is dangling loose after the spark.
Continuity mistake: The side of the mountain with the bridge is irregular with rough edges when seen in the wide angles, but smooth in the close-ups.
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