Continuity mistake: At the beginning of the movie, the car the characters take to the party has European plates. Later on, the plates are American.
Plot hole: The Hellworld website at the beginning of the film has eerie music and also Pinhead's voice reciting some of his famous lines from other Hellraiser movies, which is impossible; there's no way that someone could have gotten recordings of those moments in the past where he said the lines, so they couldn't be playing on an internet webpage.
Continuity mistake: When Adam's father starts playing with the box at the end, he has a just-lit, long cigarette in one hand. The shot cuts for only a second and the cigarette has burned down almost to his knuckles.