Plot hole: Since "Dorothy Michaels" does not exist, she will not have a Social Security number. Even with her agent acting as a go-between, the television production company, her employers, would have to have this for their records. Supplying a false Social Security number is a very serious offense (and is instantly detectable), as is employing someone without one.
Plot hole: When Ching and Jen Moo are confronted by the God Skills Society at the Sun Family Temple, there are three disciples appearing behind the master. But only two of then (the long-haired man, and then the monk) are seen entering the fight; the third one suddenly appears as a yellow-clad corpse at the entrance stairs as Ching fights the long-haired man.
Plot hole: In the very beginning at the mall, where the older guy comes in to the pizza shop and sits in Stacy's section - the co-worker says "she's not even in high school yet." First of all, the school she's at is "Ridgemont High", and secondly, if she wasn't in high school (which would mean she would be younger than 15 at least) - how could she have a job, where the minimum age is at least 15? Even by mall standards, it's doubtful they would hire someone who is 14.
Suggested correction: In the 80s, high schools in most California areas were 10th through 12th grade (not 9th-12th like they are today). So many students DID enter high school then at 15.