Continuity mistake: In the scene where Pinhead is in the church, he stands behind the table, and the candle to the right of him is straight. He then pushes the cross off the front, look at the candle, it is now on a slant then in a split second the candle is straight again as if it had never been touched.
Continuity mistake: At the end of the film Pinhead tricks Joey into giving him the puzzle box by posing as her dead father. As soon as she hands the box over he takes a knife (or sickle or whatever it is) from his belt with his left hand and poises to strike. Then it cuts to a shot from behind and he's now gripping the knife with his right hand.
Continuity mistake: At the end after Pinhead has 'absorbed' Elliot and Elliot pushes through to tell her to work the box, her hands are clean. Then she reaches for the dropped box and her fingers are bloody, causing her fingers to slip on the front of the box and stop her working it.
Continuity mistake: One of the chains reaches from the sewer and grabs Joey by the sweater during the chase scene. Every time the chains are used in the other films, they are incredibly accurate. One grabs Frank by the hand, as he grabs for Kirsty in the first film, and another effectively blocks Kirsty's way in the second, but now they can only grab Joey's sweater. [Pinhead deliberately makes the chains miss because he's just trying to intimidate Joey at this point. He can't kill her until she gives him the box.]