Continuity mistake: The scene in the Obi Wan nightclub when Indiana runs out of the window with Willie Scott. Indiana is running behind the gong and we see him collect Willie. In the next shot seen from behind the gong Indiana has yet to reach Willie before they jump out of the window.
Continuity mistake: During the palace dinner scene, the "snake surprise" is laid down at Willie's left side. A few shots later it's on her right.
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