
Continuity mistake: After decking Raphael for the Jose Canseco remark, Casey's baseball bat instantly changes hands between shots. (00:12:35)
ryguy_1983
Revealing mistake: A lot of times in the movie, when the turtles' mouths are wide open, you can see the cast. An example of this is the scene when Raphael wakes up in the bath tub and Leo hugs him. When Donatello tilts his head back and laughs you can see eyes, a nose, and a mouth within the mouth of the costume.
Jason VoorheesVisible 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)
ryguy_1983Continuity 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.
Phixius
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.

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)
ryguy_1983Continuity 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)
ryguy_1983Continuity 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)
ryguy_1983Continuity 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)
ryguy_1983Visible 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.
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)
Sammo
Continuity mistake: In the alphabet game of insults, Donatello calls Casey Jones "elf lips." Casey puts the monkey wrench on the radiator next to the dirty rag, but in the next shot the tool is gone from there and is in his left hand instead, so he retrieves only the rag from under the hood. (00:53:10)
Sammo
Continuity mistake: Casey Jones arrives to the save the day. Michelangelo does a Wayne Gretzky reference. Notice in the background Master Tatsu, solitary and surrounded just by old abat-jours and other dusty curio. When he orders in his spartan English to "attack", he suddenly has a bunch of goons all over him. (00:46:05)
Sammo
Continuity mistake: When April naively asks "You guys like pizza?" in front of the manhole, her hand drops in the close-up but is still up and pointing in the wider angle. (00:25:40)
Sammo
Other mistake: The clock behind the couch April rests on (and crawls terrified on when she wakes up) indicates 5:35 for much longer than a minute. (00:21:30 - 00:23:00)
Sammo
Audio problem: In the Italian dub, Chief Sterns reads Mr. Pennington's number as 555-5219 instead of 555-5214. (00:28:30)
Sammo
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)
Sammo

Revealing mistake: When the Turtles make their triumphant entrance jumping in frame after the logo, at the bottom of the screen you can tell they are wearing white socks/shin guards, except Raphael who is the one the camera is focused on. (00:05:30)
Sammo
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)
Sammo
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.