Factual error: In the area with the lava Willie is put in a cage and lowered over the lava. She keeps dropping down until she is stopped what looks like a few feet above the lava. In reality she would have been incinerated by the heat.
Factual error: In the scene at the end of the movie on the bridge, the fear of heights is increased by the shots of hungry reptiles waiting below. The reptiles shown are alligators. This is wrong: crocodiles are the animals that live in India, not alligators. (01:45:35)
Factual error: When they fly from Shanghai (southern China) to India (southwest of China) you see the plane passing the Great Chinese Wall. But the wall is placed in northern China, not on the route Shanghai - Chungking - India. (00:14:35)
Factual error: The British / Indian troops at the end of the movie are using Lee Enfield no4Mk1 rifles. These didn't go into production until 1940. Also India never used the no4Mk1, they used the no1Mk3 until the 1950s.
Factual error: Neither Willie nor the human sacrifice victim show signs of significant perspiration when being lowered to the lava. They should have been sweating profusely after being close to the lava.
Factual error: Indy rescues Willie from the lava pit and immediately releases her from the cage. In reality the cage would be too hot to touch for several minutes after being that close to the lava.
Factual error: The village Indy floats into, supposedly in north India, is populated with people who speak with Indy in Sinhalese, the national language of Sri Lanka. The film was shot on location in Sri Lanka.
Factual error: It seems highly unlikely that a whip trapped around a ceiling vent can lift up a 150 Kg (300 pounds) muscled man without breaking, or even without making a crack on the ceiling.
Factual error: When they are riding the life raft off of the top of the snow-covered mountain watch how it falls. All three people were close to the front of the raft, yet the raft drifts backwards before plunging in nose first. That would be impossible with all of the weight shifted to the front of the raft to begin with. (00:18:25)
Factual error: The image of the plane's instrument panel shows a VOR, just to the left of the orange circle with the triangle in it. The VOR is "a type of short-range radio navigation system for aircraft, enabling aircraft with a receiving unit to determine its position and stay on course by receiving radio signals transmitted by a network of fixed ground radio beacons. ... Developed in the United States beginning in 1937 and deployed by 1946..." (Wikipedia). The movie's opening scene is Shanghai, 1935. (00:16:45)
Factual error: After Willie and Shorty step on mola Ram's hands and make him fall off the bridge, a jet airplane is seen on the right side.
Factual error: They escape from the plane using a life raft and fall a considerable distance (looks like hundreds of feet) before landing on a snowfield. They then slide down the snow and off a cliff before landing in a fast flowing river, again falling a considerable height. There is no way they would be able to fall that distance and land on snow covered ground or a river without being killed or seriously injured, but they are completely unscathed.
Factual error: The self inflating boat on the "South China Air" plane is the typical modern colour yellow and modern shape, which didn't exist at that time.
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