The morning after Channard resurrects Julia, we see her standing at a mirror, and the whole of the floor beneath her is carpeted; yet when Channard walks across it, his shoes still sound as if he were stepping on hard flooring.
When Channard kills the original Cenobites, the collar of Pinhead's outfit undergoes visible changes. First it leaves his throat exposed but covers the rest of his neck. After Channard turns him back into a human, the collar then covers his entire neck. Finally, the collar completely disappears a second before Channard slashes Pinhead's throat.
When we see Julia in Channard's house, she is dripping blood, as she is skinless. From where she is standing, she would have had to walk across the room, dripping blood, but the carpet is very clean, excluding the area where she is standing.
The police sent out people to get evidence, like the mattress where Julia died on. They get in Kirsty's house for the evidence. Which should be impossible. At the end of the original Hellraiser the house was clearly completely destroyed.
As Kyle leafs through Dr. Channard's scrapbook, he lingers briefly on a cutting headed "Is Death the Fourth Dimension?" However, the text of the article beneath this is about a new NASA space station and is completely unrelated to the headline.