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.
When Kirsty is in Hell looking at the photos of her family & the blood begins to flow she takes a few steps back & is standing next to some debris. The dresser then falls but Kirsty is nowhere near it. It should have landed on top of her. We see a piano to her left but when the room begins to spin the piano has disappeared & there is a sofa next to her instead.
A key plot point revolves around cenobites having their memories of their former (human) selves erased after their conversion ... except that Channard-Cenobite recalls his perfectly well, evidently even after having his brain pureed by Leviathan.
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.