Continuity mistake: When Lloyd wheels out his camera and begins filming, you can see that it's a Betamax. When the cute little kid holds up the video tape produced by that camera, it's a VHS tape. (You can tell because it fits neatly inside the box. Beta tapes were entirely different dimensions from VHS and a Betamax wouldn't fit in a VHS box.)
Visible crew/equipment: After Christian Slater pulls up in the red car at the golf resort while Billie and Lloyd are arguing about stealing a car, Billie is eventually chased by cops. After Billie and the cops go through the wooden gate/fence, Billie is seen running down the street. While the camera is panning over to show Billie running from the in-car view, you can see the lens hood of the camera in the outside mirror.
Other mistake: The posters and DVD / Blu-ray covers with Billie Jean are different. Her lone earring's on her right ear when in the movie it was on her left ear. Her bangs are combed to the left instead of right and her armband's on her upper left arm instead of her upper right arm.
Suggested correction: Something being different on the poster or DVD cover is not a movie mistake.
Factual error: The movie takes place in Corpus Christi, Texas located in Texas' southern section. Characters are shown speaking with heavy southern accents despite most real life residents sounding nothing like this.
Audio problem: Just after Binx shoots Mr. Pyot, Hube says, "Don't touch him!" When Billie Jean bends down, the camera cuts to Hube who reaches for the phone saying, "I'm calling the police," but his lips don't move. (00:18:40)