In this film, The Pinhead Cenobite's objectives are stated. He wishes to destroy the box that can send him back to hell, and stay on Earth. At the beginning of the first Hellraiser, Pinhead, after poking through the remains of Frank, solves the box himself, and sends himself, along with the other Cenobites, back to Hell. The new Cenobites made from Joey's friends can remember exactly who they were, and even conversations that they've had before the transformation, yet at the end of the second Hellraiser, Pinhead doesn't remember who he is until Kirsty hands him a picture of his former self, and gives the Cenobites a lecture.
Pinhead is able to return to earth in the form of a statue.
This is supposed to be the same statue as the one that rose up out of the mattress at he very end of the second Hellraiser, but that statue was made of wood, and was covered with living images of Hell, while the statue in this film is about four feet taller, and now made of solid stone or marble. When Joey's television set is flipping through the channels all by itself, on one of the channels is an interview with Tony Hickox, the director of the film. Also, after the television is through telling Joey of the carnage at the club through the newscast, there's a pan to her floor, showing that it's unplugged. At one point, Pinhead pulls nails from his head. These nails not only miraculously grow back, but are much longer than the ones we saw hammered in at the beginning of the second Hellraiser.