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.
Continuity mistake: Before the water tank falls, there's a shot on Mola Ram and his people next to it. Then there's a wide shot of the tank about to burst and the people running away from the area. Then the previous shot of Mola Ram standing calmly with his men by the tank is repeated, which makes no sense.
Continuity mistake: During the mine cart scene, Indy is sometimes seated on the back, others on the front, with no logic whatsoever, and sometimes between one frame and another.
Continuity mistake: When the rickshaw crashes, the sailor jumps out. One second later, from a different angle, he is inside the rickshaw jumping out again.
Continuity mistake: When Indy is in agony surrounded by candles, the three next to his feet change positions between shots.
Continuity mistake: When the three are leaning on the mountain with the jet of water, Short's arms are spread apart in the wide angle, but close to his body in the immediate close-up, a frame later.
Continuity mistake: When the pilots jump off the plane the flowers on Willie's hair swap positions for a brief moment.
Continuity mistake: While eating in the Indian village, Short's hat swaps back and forth from tucked down to his eyebrows or raised up, with his fringe visible.
Continuity mistake: While hanging off the bridge, Indy's shirt keeps changing from light to dark, and from very dirty to slightly dirty all the time.
Continuity mistake: The raft arrives in a big place with no snow, yet from the opposite front angle there's snow all around.
Continuity mistake: When Willie falls from the elephant into the puddle of water, her hair varies from very wet at the bottom to mostly dry from each different camera angle.
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