Continuity mistake: En route from the front door of Wayne's mansion to the table in the Batcave, the pile of pizza boxes in Alfred and then in Mike's hands continues to change in size and number: at first the pizza girl delivers 11 boxes, Mike slams on the table just 8, but he brought down the stairs twice that amount (without counting through freeze-frame the precise numbers, it's simply obvious at first glance that the pile is bigger in some shots and the pizzas themselves are pictured of inconsistent size).
Continuity mistake: Michelangelo gets part of his mask's tie off blown off by the Penguin, making it shorter than the other. Within minutes it's back to normal when they meet Batman.
Plot hole: None of the Arkham inmates other than Poison Ivy should've mutated. The stuff only mutates you into a half human half animal creature, etc., if you've recently touched an animal or plant like Ivy did.
Continuity mistake: After Batman beats the hell out of Shredder, he's got blood all over his face. When the machine crashes down and launches him in the air into a pipe and he falls back down towards the camera, for a few frames you see his face again, and there is no blood. But in the very next shot before he falls into the chemicals, the blood on his face returns. (01:21:00)
