Continuity mistake: When Short starts to jump on the bridge, the part where he's standing is in the shadows, while the rest is on the sunny side. When he falls through the hole, the whole bridge is shadowy.
Continuity mistake: During the fight on the conveyor belt in the mine, the buckets and huge rock used to defeat the bearded giant keep changing positions all the time.
Continuity mistake: Short is in the mine pretending to hammer some rocks and a guard whips at him. Short's fringe style is different depending on which angle focuses.
Revealing mistake: At the bar Indy has swords thrown at him. The string to make them fly is visible attached to the sword on the left side. Also, the swords disappear in the next angle.
Continuity mistake: After the Indians fire arrows at the bridge, Willie and Short step repeatedly on Mula's hands. The position of his hands changes from spread apart to close together from one frame to the other with no movement in between at all.
Continuity mistake: In the mine, while Short punches the Maharaja, the Thuggee smashes a rock against Indy's head, turning it to the right side. A frame later, from a wider angle, Indy is turning his head to the opposite side.
Continuity mistake: In the raft, Willie's hair changes from soaking wet to dry and fluffy right after saying, "I hate you!"
Continuity mistake: During dinner, after the British soldier dips his finger in the cup, Indy's position swaps between frames from looking straight with his right hand raised, to looking to the left side with his hand lowered.
Visible crew/equipment: When Willie is brought the soup, many stage lights are reflected on the tureen, and the guests seated in front disappear.
Continuity mistake: Indy's raft lands on the water, and he is ducking but rises up and rows with his hands for a couple of seconds. Then a frame later he is still ducking and rises up again.
Continuity mistake: The three arrive at the palace and are greeted by the Prime Minister. Willie raises her right arm to move her coat to her left hand. Before she finishes her movement, the angle cuts and she already has the coat under the left arm.
Continuity mistake: Indy crashes against the orchestra, musicians, instruments and decoration. Two seconds later everything and everyone manages to be perfectly back in place.
Continuity mistake: When the baddie hands Indy the diamond, the black napkin in front swaps from wrinkled to straight.
Revealing mistake: When Willie and Short escape the jet of water and Indy climbs the mountain alone, the river below is totally still (impossible because of the huge amount of water that's falling on it), revealing it's a still image.
Continuity mistake: When the three walk towards the palace, they pass by a wall with an elephant painted on. Round the corner, a guard stands 10 meters in the back. A frame later, the guard stands right next to the three. In the following shots he keeps appearing or disappearing randomly.
Revealing mistake: After Indy drinks the antidote, many of the chase-scenes are obviously sped up, watch the way the actors move.
Continuity mistake: In the plane, Willie wakes up Indy, who asks if they've arrived, and a feather lands on his head. A frame later the feather is gone.
Continuity mistake: In the raft, after Willie asks where they are, the coat she holds changes positions between one shot and the other.
Continuity mistake: Short falls through the hole and there's a POV shot of his legs moving wildly while he cries "Help!" Then he is rescued by Willie and lifted up safely, his legs now still, and his nerves calmed. However, the very same shot of the wild legs and the cries for help from before is suddenly inserted, which makes no sense whatsoever.
Continuity mistake: During dinner, a man in front of Willie asks her is she isn't hungry. The way he holds the huge beetle swaps from straight to sideways between angles.
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