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.
(at around 1h 22 mins) 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.
(at around 1h 4 mins) When Dr. Channard is being turned into a cenobite, his tie disappears in some shots.
(at around 6 mins) During Elliot/Pinhead's torture and creation scene, the cutting makes his facial scars briefly vanish then reappear.
(at around 34 mins) 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.
(at around 1h 30 mins) If Kirsty is wearing Julia's skin, how is she able to sound like her?
(at around 1h 2 mins) When Kirsty is in the maze, she runs into a brick wall which is obviously fabric.
(at around 27 mins) 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.
(at around 1h 9 mins) When Frank is in his own private Hell, he throws Kirsty against the wall and it gives like it's made of soft material.
(at around 52 mins) When the Cenobites appear in Dr. Channard's office, the curtains are ripped away from the window, and you can see the string that rips them away.
(at around 1h 18 mins) When the Channard Cenobite bursts through the window in the hospital room, it's clearly a stunt double.
(at around 1h 29 mins) When Tiffany returns the box to its cube shape near the end, the Channard Cenobite's lips are not moving when he says "Your case is closed, Tiffany."
When Kirsty is in her mother's house and the room begins spinning after the blood-soaked cabinets fall to the ground she can be heard saying "Somebody please help me!!!" but her mouth is wide open at this point and is clearly not moving to the sound of the words that she is meant to be saying.
(at around 1h 28 mins) When Kirsty sees Tiffany on the ledge and Leviathan makes rushing wind blow, the wall behind Kirsty ripples like it's made of fabric.
(at around 31 mins) When Julia is resurrected, a camera can be seen moving behind the desk by the curtains as the injured man crawls toward it.
The epilogue in Channard's house, with the removal men taking away his occult possessions and encountering the bloody mattress, stretches plausibility. Considering the attic full of rotting corpses, the house is as much a crime scene as the Cotton house was in the first act, and ordinary removal men would not be invited in to manhandle the evidence.
In the first film, the Cenobites are only referred to by name twice, and only by Frank to Julia. And yet, in the second film, Kirsty refers to them twice by name, despite her having no way of knowing what they're called.