Revealing mistake: When the 3 heroes exit the mine cart and escape from the water flood in the mine, Harrison Ford is replaced by an obvious stuntman.
Revealing mistake: When the water tank falls over, the vapour fumes are moving in slo-mo, despite the whole scene moving at a normal speed.
Continuity mistake: When Mola Ram tells the Thugees to get to the huge cauldron, there's big clouds of smoke all around it, which disappear a frame later from a different angle.
Continuity mistake: When Indy throws a block of wood on the rails, it lays parallel, yet a frame later, from a different angle, it lays sideways.
Continuity mistake: When the mine cart is about to stop, Indy's left hand is alternately covered by Willie and Shorty's or not, depending on the angle.
Continuity mistake: When Indie and Willie are about to jump out of the bar's window, there are some cables along the window which disappear when they crash through it.
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: When the heroes leave the village, the shrine where the Indian is standing swaps from having a blue sky to a dark grey one, and smoke from a campfire all over.
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.
Continuity mistake: During the hanging bridge scene, the brown mountain has some white rocks on the right side which sometimes disappear, or even appear on the opposite side as when Mula Ram throws the Thuggee down.
Continuity mistake: A man takes the wooden blocks off of Laoche's plane wheels but disappears in the next angle.
Continuity mistake: When the Maharajah enters the palace for the first time he is escorted by two guards. A frame later the guards are gone from behind and are already formed along the aisle.
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: When Short starts to jump on the bridge, the part where he's standing is in the shadows, while the rest is on the sunny side. When he falls through the hole, the whole bridge is shadowy.
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: Short is in the mine pretending to hammer some rocks and a guard whips at him. Short's fringe style is different depending on which angle focuses.
Revealing mistake: At the bar Indy has swords thrown at him. The string to make them fly is visible attached to the sword on the left side. Also, the swords disappear in the next angle.
Continuity mistake: After the Indians fire arrows at the bridge, Willie and Short step repeatedly on Mula's hands. The position of his hands changes from spread apart to close together from one frame to the other with no movement in between at all.
Continuity mistake: In the mine, while Short punches the Maharaja, the Thuggee smashes a rock against Indy's head, turning it to the right side. A frame later, from a wider angle, Indy is turning his head to the opposite side.
Continuity mistake: In the raft, Willie's hair changes from soaking wet to dry and fluffy right after saying, "I hate you!"
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