Continuity mistake: Mola Ram throws a Thuggee down the bridge and Indy moves away. The angle cuts to a closer angle and Indy is in the previous position moving away again.
Continuity mistake: When the pilot checks if Indy is asleep he holds the curtain with his thumb inside the cabin and fingers on the passenger part. From the opposite angle he holds it with the side of his hand, all fingers inside the cabin.
Continuity mistake: In the mine, Indy fights against a bearded bad guy, who throws a hammer backwards that lands on a worker's head, knocking him out. The workers are very close together in the wide angle, then equidistant in the close-up when the hammer lands, and then together again in the wide angle. Also the worker that falls unconscious is standing straight a frame later.
Continuity mistake: When the pilots are about to jump off the plane, they walk between Willie and Indy. Her head swaps from tilted to straight from frame to frame.
Continuity mistake: When Short is hanging through a hole in the bridge, his shirt keeps changing back and forth from being motionless in the POV angles, to wildly flickering in the wide ones.
Continuity mistake: When Indy is first raising Willie up from the pit of lava, as he just begins to raise her up you can see that the eye hooks and rods that hold the cage are rising up out of the hole. However when we switch to the shot of Willie in the hole, she's just a few feet from the lava.
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