Maniac Cop 2 takes place immediately after Maniac Cop. Near the end of the first film we are told it's St. Patrick's Day (hence the police parade scene), but at the beginning of part 2, the police commissioner is decorating his office for Christmas just after a scene where a Christmas carol is heard by church bells. Seeing as where one movie takes place directly after another movie this is an obvious continuity issue.
When Maniac Cop kills Jack Forrest by the newspaper stand, he violently stabs Forrest's neck and throat so that the blade cuts all the way through Forrest's body. In the next scene, when Detective McKinney visits the medical examiner to view the body, Forrest has no visible cuts or injuries to his neck or throat.
When the clerk is scratching tickets for the burglar, he starts scratching the second one, then it goes to a close-up of his face and he says that it isn't a winner, then it goes back to the angle of his hands scratching tickets, and there are now three scratched tickets laying there. The clerk had only scratched two.
After Turkell is arrested, Detective Sean McKinney visits Turkell's apartment. When Detective McKinney looks at Turkell's 'shrine' to the women that he allegedly killed, the candles are still burning, but the candles should have burned down.
When Cordell attacks Teresa and Susan in the cab, Teresa fires upwards of 8 shots into Cordell from a 6-shot revolver.
When Maniac Cop throws a man into (what looks like) a thick, solid wall during the prison scene, the wall is clearly shaking.
When the Maniac Cop is getting burnt in the prison, it's a stunt man wearing protection (a bag) over his head.
When the angry cab driver is yelling at the female cop that stole his taxi, the words you can hear him saying do not match is mouth.
At the Police Station, as Cordell walks through the walls made of glass, the second one clearly shatters before he walks through it. Also, in the same scene a minute later, you can clearly see the wire used to drag the officer through the wall frames.
After Susan Riley is handcuffed to the steering wheel of a car and it crashes, a rescuing cop calls for a hacksaw to cut off the handcuffs. But any cop would have a handcuff key and could have freed her easily.