Continuity mistake: Near the end when the Turtles are fighting Shredder and Splinter makes his appearance, you can see Mikey starting towards Splinter only to be held back by Raph, then a few seconds later, when Leo rolls to the group, the scene happens again, Mikey heading towards Splinter with Raph pulling him back. (01:22:28)
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). (00:44:15)
Visible crew/equipment: Just before the ceiling collapses on the antique store a boom operator can be seen on the right hand side of the screen.
Factual error: April interviews (live) the police Chief and then tries to take the train back home. The subway station shows that it's the City Hall stop, and she just finished her interview with the guy, which happened mid-afternoon as you can see by the clock in the corridor. Despite being New York in the middle of the day, there's not a soul in the station, nobody got off the train she just missed, nobody around at all on any of the multiple platforms. It's a trope good for a scene set at 3 AM, not 5 PM. (00:19:25)
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. (00:38:15)
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: When the turtles are fighting Shredder, in the second go-round so to speak, the order is Donatello, Michelangelo, Raphael, and finally Leonardo. When Leo is knocked to the ground, the next shot shows him leaning over the edge of the building as Donatello walks into shot holding his shoulder as if he just did battle.