(at around 46 mins) Pinhead, after being stomped on, is in the next scene locked in a cage next to Blade.
When the pieces for the new puppet are being carved they are wood, when the puppet is finished it is metal.
At approximately 52 minutes into the movie, Jane is holding Pinhead, but the footage shows him standing in front of an entirely different setting.
Leech Woman is seen in this entry despite being set on fire in the second Puppet Master movie, Puppet Master II (1990).
(at around 19 mins) When Sheriff Garvey meets Tank outside Dr. Magrew's house Garvey says, "Don't you worry". You can clearly see the boom mic at the top of your screen at that time.