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.
Suggested correction: It was actually in a room in the institute. Not hell. Easy enough to retrieve it.
Deliberate mistake: As Joey is running down the street and having things blow up all around her, you can see other people walking on the sidewalk not reacting to the destruction around them, even when something blows up just a few feet from them.
Deliberate mistake: The film was supposed to be taking place in New York City yet you only see NYC twice when Joey is riding the city bus and another view of the Twin Towers during another scene. Yet is obvious she is not in New York City after running from the Boiler Room and being chased by the Centobites. Even the police cars and uniforms are not NYPD they say Summit Police. Also, if that kind of destruction was going on there would be several more than only two cruisers and three cops.