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.
Deliberate mistake: Joey finds Channard's photo of Capt. Elliot Spencer in the closed art gallery but Kirsty stole that photo and gave it to Pinhead in the second film, where it was left on the floor of Hell. Also, all the sketches of the box were amongst the things from Channard's institute but those pictures and the other similar ones were from Dr. Channard's home collection. They were never kept at the institute.
Revealing mistake: After Joey runs from the club into the street and a car swerves to avoid her, it hits a lamppost which causes sparks; but look closely and you can see that the sparks appear just a split second before the car actually hits the post. The sparks were rigged and set off a second too early.
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.]
Revealing mistake: When Pinhead kills Sandy, his chains attack her, then they lift her up, and her stunt double is visible because her hair is much shorter and her face is completely different.