Actor Allusion: The character played by Janet Leigh gets in a car that is similar to one she drove in Psycho, with a piece of film's score playing in the background. She also tells Laurie that the shower is clogged - a reference to her character's famous death in the film. The character was intended as an Actor Allusion to PJ Soles - as it was named after her character from Carrie.
Recut: There's a TV Cut that trims the violence and cuss words, but also has some alternate scenes. One added scene gives the counselor played by Alan Arkin some development by revealing that his mother cheated on his traveling salesman father, and he got blamed for knowing, but doing nothing.
Throw It In: LL Cool J ad-libbed the line "and comb your hair", inspired by Josh Hartnett's messy hair.
An earlier version of the script didn't ignore the previous three films. A scene was planned where a student in Laurie's class would give a report titled 'The Haddonfield Murders' about Michael Myers's pursuit of Jamie Lloyd. Afterwards, a heartbroken Laurie would go to the bathroom to vomit. This was later abandoned so the film could exclusively focus on the Laurie Strode part of the franchise.
PJ Soles, who played Lynda in the first film, was the original choice to play Laurie's secretary. The character's name Norma Watson was intended as a Shout-Out to Soles's Star-Making Role in Carrie. She dithered for a while about whether to take the role and they eventually asked Janet Leigh after Soles failed to give them an answer.
John Carpenter was originally considered as a director. But after disagreements about money, he walked off the project.
The killer's death had multiple original possibilities - including Laurie trapping him in between a retractable gym floor and then stabbing him with a javelin - or being eventually cut in half by a helicopter's rotor blades.
The killer in this was intended to not be Michael Myers at all, but a copycat killer (and this would be explained in the next film). Ultimately Halloween Resurrection explained that Myers had switched places with a paramedic last-minute instead.