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)
Revealing mistake: When Casey Jones gets off the garbage truck he rammed the fire escape stairs with, he punches two ninjas, but they go down (especially the first) before his fists connect (or rather don't connect). (01:21:10)
Revealing mistake: When Don tries to be hip shouting "Bossa Nova!" at the back of his open mouth you can spot the white of the teeth of the actor inside him. (00:05:40)
Revealing mistake: In the first, unseen, appearance of the Turtles in the movie, Raphael saves April breaking the streetlight with his sai. The lights go out a good second after the bulb is supposedly shattered, though. (00:03:55)
Revealing mistake: During the Turtles fight with Shredder watch carefully, the blade on his left hand bend back, made of rubber.
Continuity mistake: After Master Tatsu kicks his opponent in the face, a couple of bystanders in the background instantly move further apart from each other between shots. In addition, one of them is a Foot member who loses his nunchaku as the shot changes. (00:32:30)
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)
Continuity mistake: After decking Raphael for the Jose Canseco remark, Casey's baseball bat instantly changes hands between shots. (00:12:35)
Visible crew/equipment: As April walks from the bathroom trying to get Charles off her case, the top of a camera operator's head is briefly reflected in a mirror above the aquarium. (00:29:50)
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.
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)
Revealing mistake: When Raphael wakes up, and Donatello is laughing, when he opens his mouth, the actor's mouth inside the turtle's mouth. (00:56:25)
Continuity mistake: As he shouts down to Michelangelo through the sidewalk grate, watch how the pizza man's $10 bill changes from left hand to right in between shots. (00:10:20)
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: Michelangelo and Donatello are standing side by each after Shredder introduces himself on the rooftop. But one shot later when Raphael steps in to take on Shredder, Donatello is now behind Michelangelo instead. (01:18:35)
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.
Audio problem: While Casey fends off the Foot Clan in the antiques shop, an answering machine falls from April's apartment above, hanging by its power cord. Charles' voice can be heard on the speaker, but after the cord snaps his voice can still be heard finishing a sentence. (00:46:50)
Visible crew/equipment: When Michelangelo retracts his head from a sword blow into his shell, you can see a crewman's hands under his armpits, holding and moving his upper arms.
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.
Answer: Most likely to kill Shredder and make sure that there would be no way to come back but, as seen in the sequel, Shredder does return.