Revealing mistake: There's one scene where they are surrounded by the foot. Leonardo reaches behind him for his katanas, but he doesn't unsheath them. If you look at his elbows, you can see gaps in the pads where the actor in the suit hasn't fully fastened the gloves to the rest of the outfit.
Continuity mistake: When April arrives at her apartment, she places down a folder like object, and then puts some paper and her keys on them. Next she places her purse on top of the left side of the objects. Moments later, after she goes upstairs, the Turtles come in through the window next to the stuff she sat down. Now the purse is on top of the right side of the items, and the strap is in a different position.
Continuity mistake: When the Turtles first arrive on screen behind Keno, they leap over the boy to attack the thieves. Their order from left to right when they walk up is Mikey, Leo, Donny, then Raph. The very next shot shows them in the air, and the order is now Mikey, Donny, Leo, then Raph. Donny and Leo switched places between shots.
Other mistake: During the fight scene in the TGRI building, when Michelangelo has the ooze and gets jumped for it and loses it, watch the bottom of the screen. Donatello is lying down and trying to get up. But in the next shot he's up and kicks out the ooze from the foot soldier.
Continuity mistake: The Ooze canisters look completely different from the first movie. The canister in Splinter's flashback was the same shape but had a different label, marked "Radioactive Material" with black and yellow bars. In this movie the canisters had a plain TGRI printed in black. Also Splinter refers to the canister as being broken in half, but in his flashback it is intact.