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 (1976).
Likewise Norma's motherly attitude towards Laurie was intended as this, to serve as a nod to the fact that mother and daughter were starring alongside each other.
Follow the Leader: Much of the film is heavily influenced by Scream, which had revived the slasher genre just over a year before this film came out. Dimension Films (who produced both movies), got Kevin Williamson (writer of Scream) on board to produce and write this film. Even it's original musical score from John Ottman was largely scrapped in favor of recycled music cues from Marco Beltrami's score for Scream. Both films largely follow the same formula with an "opening victim," snarky references to other slasher films, cameos, and Michael Myers was even supposed to be a killer-in-disguise in the original script (see below).
The Other Darrin: Due to Donald Pleasance dying shortly after the sixth film, Dr Loomis's vocals are done by a sound-alike actor Tom Kane.
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.
Interestingly, some aspects of this version do remain in the final script. For instance, in Halloween 4: The Return of Michael Myers, it's explained that Laurie had died in a car accident. H20 retconned this by explaining that she faked her death. All of this is kept in the final version of the movie, as it was too ingrained in the film's plot and message to do away with.
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 (1976). 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.
The movie Sarah and Molly have in their dorm room would originally have been So I Married an Axe Murderer. The joke would have been that they were watching a movie starring Mike Myers.
The role filled by Nancy Stephens - reprising her part as Marion Whittington (nee Chambers) from the first two films - was originally for a new character. It would have been the daughter of Dr Loomis, Rachel, whose house is broken into.
Likewise a subplot featuring two detectives tracking Michael for Marion's murder was cut from the film. As such they only appear in one scene and are promptly forgotten.