At the end, when the British Indian Army Riflemen fire at the Thuggees, because they are using blanks, which have no recoil, one rifleman is short-stroking his rifle. He is only drawing back the bolt 3/4 of the way before the brass breaks loose from the extractor claw, then tries to load a fresh round before he has expended the spent brass. This causes both rounds to jam in the chamber, and takes him several seconds to clear it by pulling back hard on the bolt.
This, along with Gremlins, is partially responsible for the making of the PG-13 rating because of its dark content.
Temporarily banned in India due to its offensive representation of their culture. The writers claimed any inaccuracies were supposed to be deliberate clues that Mola Ram was evil.
Not a ban, per se, but the uncut version of the film wasn't released in the UK until the 2012 Blu-ray. Previously, about one minute of violence and gore was cut in order to secure a PG rating as the 12 rating didn't exist at the time. (As noted above, there was also some drama about the rating in the US.)
Creator Backlash: Spielberg has stated in his interviews that Indiana Jones and the Temple of Doom was his least favorite of the Indiana Jones films, and the best thing about it is that he met Kate Capshaw while making it. In the 2003 documentary about the film, Capshaw was very critical of Willie's character, saying that all she does is scream.
According to some sources star Harrison Ford himself was not entirely comfortable with the film's story and, again, according to some sources, he was not entirely happy with how the film turned out either.
Creator Breakdown: The film was produced while Lucas was going through a divorce, as well as Steven Spielberg's then-current breakup with Amy Irving, hence the scene where a sacrificial victim gets his heart ripped out and set ablaze. Lucas has admitted that this may be why the film was made so much Darker and Edgier than its predecessor. It may also explain why Willie is an annoying collection of sexist stereotypes as opposed to the somewhat better female characters in the other films.
Dyeing for Your Art / Dye Hard: Prior to Temple of Doom, Amrish Puri had quite the full head of hair. His role as Mola Ram was so iconic, he kept his head shaved from then on.
Fake Shemp: As Harrison Ford injured his back while filming the scene where Indy is being strangled in his room, stuntman Vic Armstrong did as many scenes as possible while Ford recovered, even those the actor could have done easily.
Mean Character, Nice Actor: The late Amrish Puri, the Indian professional wrestler turned-actor, who played the heart-ripping Mola Ram in Indiana Jones and the Temple of Doom, and went on to play several Bollywood villains, is said by both Harrison Ford and Steven Spielberg to have been a sweet and lovely man.
Reality Subtext: Around 1984, George Lucas went through a particularly vicious divorce, and Steven Spielberg went through a rather nasty breakup. This led to the film's darker tones, and, in particular, Mola Ram ripping out people's hearts.