Revealing mistake: When the water floods the mine, some shots of the 3 heroes are an obvious composite of their blue screened image over a set. Problem is, when Indy tells the two to run towards a tunnel on the right with a log blocking the way, Indy and Shorty run through the log as if they were ghosts.
Revealing mistake: After Indy escapes from the conveyor belt, he runs on some suspended planks while being shot at. Watch the planks: There's black masking tape where the explosives are (which disappear in later shots). Furthermore, right before he takes out his whip, he grabs a railing where the bullet has just hit, and you can see that the black tape is dangling loose after the spark.
Revealing mistake: When Indy is hanging on the cliff as it falls out from underneath him (right after the mine cart scene), as he's kicking, you can see the stone wall moving in and out as he hits it after the rocks fall out underneath him.
Revealing mistake: When Indy is put inside a cage Short Round comes to hug him. There's a shot of Indy from behind and he is a noticeable stand-in: Thinner face, clean hair, no sweat, and clean shaven instead of stubble.
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.
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.
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.
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.
Revealing mistake: When Willie and Short escape the jet of water and Indy climbs the mountain alone, the river below is totally still (impossible because of the huge amount of water that's falling on it), revealing it's a still image.
Revealing mistake: After Indy drinks the antidote, many of the chase-scenes are obviously sped up, watch the way the actors move.
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