Revealing mistake: When Indy is whipped six times, the first time we can see the whip doesn't touch him, or go anywhere near him.
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.
Revealing mistake: When Indy wraps his whip around an assassin's neck and hangs him on the fan, we can see it's not actually around his neck, it's just attached to his clothing.
Continuity mistake: When Indy punches Short Round, he starts falling forwards, but lands on his back.
Audio problem: Indie lifts Willie from the lava pit, she is semi unconscious. She slaps him weakly but instead a loud and strong punch is heard.
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