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.
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.
Continuity mistake: In the mine cart, when Indy hits a tank with a shovel, the Thuggees behind raise their arms, yet a frame later, from a wider angle the arms are lowered.
Continuity mistake: When Willie and Short get to the bridge there's a big tree on the left. In subsequent shots it's gone.
Continuity mistake: During the first Thuggee ritual, there are two Thuggee Priests next to the wheel and lever. However, when the cage with the Sacrificial Victim is lowered, one of the priests disappears.
Continuity mistake: After the pilots bail out, the main engine has already stopped with the prop blade between five and ten degrees off-center, angled right. In the shot before Indy and company bail out, the prop is angled left, then right again.
Continuity mistake: At the start of the mine car chase look at the length of the braking poles on the side of the car. When they leave the main cave the roof lowers and the braking poles are slightly higher than the side of the car but were a lot longer to start with.
Continuity mistake: When that guy is lowered into the lava pit, the cage is level horizontally. When the empty cage is raised again, it's slightly at an angle.
Continuity mistake: During the mine cart chase, Indy hits one of the switches, putting it from the forward to the back position. When the guards in the mine cart get close, they shoot it, putting it from the front position to the back position again.
Continuity mistake: As the Thugee ceremony comes to an end, you see the stage hands exit and the spectators get up and start to leave. The next scene shows Short round looking over the edge and the stage hands are still on the stage, just starting to leave and some of the spectators are still in the process of standing up to leave.
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