Continuity mistake: When Indy is fighting the Chief Guard on the conveyor belt, there is nothing behind the guard before he picks up the large rock, but in a close-up there are now small rocks on the belt.
Continuity mistake: When Indy hangs the assassin on the fan, in one shot he's spinning, but in the very next shot he's not. He can't just instantly stop, he'd have to slow down.
Continuity mistake: When Indy punches Short Round, he starts falling forwards, but lands on his back.
Continuity mistake: On the bridge, when Indy threatens the Thugees to drop the bag, they're a couple meters away from his back, but in the next angle they're further away.
Continuity mistake: After Short Round breaks the Maharaja's spell, the blood on the side of his mouth swaps from a thick strand to a thin one between shots.
Continuity mistake: Mola Ram falls off the bridge-ladder when a step breaks in two, but from the immediate wide angle it just moves slightly out of place. Furthermore, in the next angles the step is perfectly fixed.
Continuity mistake: When the three heroes arrive at the village there's not a single bit of grass around. When they leave the place the morning after there's vegetation everywhere.
Continuity mistake: The movie starts with a guy playing a gong, holding its hammer from the lower part. A frame later his upper hand is holding the hammer from a much higher position.
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: 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: 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: When Mola Ram is climbing the bridge, Willie and Short stand together; half a second later Mola Ram falls and Short has managed to climb up and move apart to let him pass by. Then a nano-second later, Mola Ram grabs onto a piece a wood and Short and Willie manage to stand together again. (01:41:15)
Continuity mistake: On the bridge, an arrow suddenly appears to the right of Indy's foot seconds before any arrows are shot at him. (01:42:55)
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