According to John Carpenter and Kurt Russell in the DVD Commentary, the story was originally written as a western but Carpenter decided to set it during modern times. They even mention that instead of Jack Burton's truck being stolen, it was originally his horse.
The Brides of Lo Pan must have green eyes. Yet both Kim Cattrall and Suzee Pai had brown eyes in real life. Both wore green contacts for the movie. This is very obvious in the hi-def version of the movie.
Both John Carpenter and Kurt Russell explain on the audio commentary that the test screening was so overwhelming positive that both of them expected it to be a big hit. However, 20th Century Fox put little into promoting the movie and it ended up being a box office bomb. However, it went on to be a huge cult hit through home video. Carpenter and Russell explained that the reason the studio did little to promote the film was because they didn't know how.
Kurt Russell confessed on the DVD commentary that he was afraid of starring in the movie because he had made a string of movies that flopped at the box office. When he asked John Carpenter about it, he told Kurt that it didn't matter to him - he just wanted to make the movie with him.
The vehicle Egg Shen drove in the movie was a 1936 White touring car. That very car is now in Yellowstone National Park (the location it was originally built for), named 'Hollywood', and gives tours out of Old Faithful.
The short knives wielded by the "Three Storms" warriors, that Thunder calls "Hui Huan Dou" (Soul-Returning Blades) are in fact Nepalese Kukri. These knives were made famous for their usage by the Gurkhas in the British Indian Army.
The name of the murdered gang leader, Lem Lee, is probably a reference to Tom Lee, the leader of the On Leong Tong, a crime syndicate in New York's Chinatown in the early 20th Century that fronted itself as a merchant association.
This the last studio film that John Carpenter worked on at the end of the 1980's due to the problems he'd received during the production of the film with then studio head Lawrence Gordon, who practically interfered with the film up until its release date. Prince of Darkness (1987) and They Live (1988) would be made independently through Alive Films without any studio interference and distributed by Universal Pictures.
According to John Carpenter on the audio commentary that the opening of the film with Egg Shen (Victor Wong) in the lawyer's office was added in as a request from 20th Century Fox because to make Kurt Russell's character Jack Burton to be more heroic. If the scene was not added in, the film would have started with Jack driving to San Francisco.
The trivia items below may give away important plot points.
As Lightning (the character, one of the Three Storms) is crushed to death near the end of the film, some of the lightning he emits forms a small Chinese symbol as it disappears (near the top middle of the screen). The symbol translates as "carpenter". This film was directed by John Carpenter.
In the DVD Commentary, John Carpenter jokingly says that Kurt Russell's character Jack Burton is the hero of the movie, but other than killing Lo Pan and saving Wang when he shoots the guard, he is more of a sidekick throughout the movie.