The name Jen Danzig is a reference to Glenn Danzig, the former singer and leader of The Misfits, who wrote and sung the songs Halloween and Halloween II after the original movie was released. The two songs have nothing to do with the movies, because their lyrics do not even touch the main plot.
Jamie Lee Curtis agreed to do her part, only to make sure her character, Laurie Strode (or herself) wouldn't appear in another sequel. (At the time of the film's initial release, executive producers Malek Akkad, and Moustapha Akkad tried to explain it by claiming Jamie Lee Curtis "was so impressed with the screenplay, that she wanted a large part in it". She has publicly stated that was not the case, she was under contract to do it.)
Michael Myers is not given credit for any of the murders that occur in Halloweens' 4, 5, or 6. A sanitarium resident even notes that Myers was not heard from for the twenty years between the events that occur in Halloween II (1981) and Halloween H20: 20 Years Later (1998).
At the start of the film, an asylum inmate recounts how Michael Myers had stayed out of sight for "these three years", i.e. since Halloween H20: 20 Years Later (1998). This places the events of that scene in 2001 - the first year to have a full moon occur on Halloween since 1945.
This is the second Halloween film to make any sort of reference as to what exactly Michael Myers eats. In the original Halloween (1978), when Sheriff Brackett and Dr. Loomis enter the Myers house, they see something on the floor, which turns out to be the corpse of a dog. Dr. Loomis simply says "He got hungry."
Originally, the executives of Miramax wanted to continue the series by creating a whole new story of which didn't have anything to do with Michael Myers after the last film, in a similar manner to Halloween III: Season of the Witch (1982). However, poll results conducted throughout fan websites proved to the producers that fans wanted Michael Myers to return again.
The name of the psychology professor at Haddenfield University is Dr. Mixter. This was also the name of the doctor in Halloween II (1981) that treated Laurie Strode (Jamie Lee Curtis) and was killed by Michael Myers with a needle in the eye.
Several new endings were written during production and the cast was never sure how the film was actually going to end. Four different endings were filmed, and the director wanted the studio to ship a different ending to each theater, a technique used before during the theatrical release of Clue (1985). However, the studio disagreed and the endings now appear on the DVD and the Internet.