Audio problem: When the group piles into the lifeboat on the crashing plane, Shorty (who is stuck between Indy and Willie) exclaims "Indy, I can't breathe!", but his lips don't move. (00:17:35)
Audio problem: When Willie is trying to find the "Fulcrum Release Lever" she screams when Indy grabs her hand, but if you watch her mouth (just visible through her hair) it doesn't open. (00:58:20)
Audio problem: A few times during the banquet scene, various snakes make noises like squealing pigs or large bugs.
Audio problem: Indy's line "Those aren't big birds, sweetheart. They're giant vampire bats," doesn't match the mouth movements he is making at the time. (00:30:40)
Audio problem: When Indy, Willy and Short Round are leaning on the mountain where the jet of water comes out, none of their cries match their lips.
Audio problem: In the first shot of the band inside the palace, to the left of the singer, there is a guy playing the drums. He's supposed to start playing the larger drum right before it cuts to the dancers. But, the sound of the drum starts before he starts hitting the sides of it.
Audio problem: In the mine chase scene, when both carts are parallel to each other, Indy punches a thug. A frame later, from a different POV, two quick punches are heard, but no one is punching anybody.
Audio problem: While they're in the tunnels, Willie's face appears to be normal while there's a scream of her in the audio background. (01:36:05)
Audio problem: While Indy and Short are trapped in the room with the spiked ceiling, Indy takes his hand out through a hole and grabs Willie's hand by surprise. A loud cry is heard, but she doesn't mouth it nor reacts with surprise.
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