Continuity mistake: When Splinter is holding the Shredder over the building's ledge, the cord on Mike's discarded nunchaku changes position in relation to the spear's point. It moves closer to the point for a single shot, then moves back to its original position in the subsequent shots.
Continuity mistake: After Raphael has a fit and walks out of April's apartment, he goes up on the roof to vent his anger for a while. Pretty soon, Casey spots him from another rooftop several buildings away while tuning a radio. As Casey looks out at Raphael's faint image in the distance, pay close attention to the background as well as the white building Raphael is standing on (you can notice the Empire State Building among other landmarks). When Casey grabs some binoculars to take a better look, Raphael can be seen resting on a brick ledge. In the following shot Raphael looks out at the city towards Casey's vantage point, but from Raphael's position, the Empire State Building - as well as the white building where he was venting just moments before - are visible on the skyline. Somehow Raphael has managed to relocate to another building's rooftop between shots.
Continuity mistake: When Splinter flips Shredder over the edge of the building, Shredder pulls a knife and throws it. When Splinter catches the knife, he catches it with his right hand; in the next shot, Splinter's right hand releases the nunchaku and Shredder falls. The shots are out of order.
Continuity mistake: During a fight sequence between the Foot Clan and three of the turtles in April's apartment, keep in mind that April is still tending to an injured Raphael in the living room. But as the floor collapses into an antiques store below, you'll be able to spot her on the lower left side of the screen shielding her eyes from debris - instantly in the store before anyone else (except for Master Tatsu and several other Foot members, who were waiting there to begin with).
Continuity mistake: When Danny is admiring April's turtle sketches, he asks if he can keep one of them. His right hand holds onto a sketch of Leo at first, but in the following shot his right hand isn't gripping the sketch at all. Instead, he's seen reaching out to pick it up from the couch.