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)
Revealing mistake: Michelangelo dodges the axe a Foot clan member swings at him by hiding his head into the shell. When he knocks his assailant out with a backhand, you can see a large gap between the mask and the rest of the suit. (01:17:30)
Revealing mistake: When Michelangelo and the foot soldier are having their nunchaku duel, you can see the foot soldier's weapon is foam padded so as not to injure the performer.
Revealing mistake: When Raphael is fighting the Foot Clan on the roof of April's building, after he tells them that they must be studying the abridged book of ninja fighting, he kicks one of them in the stomach and then cartwheels over his back to kick another one in the face. You can tell he misses the second one by a mile, but the man still groans and collapses unconscious into the chair behind him. (00:40:45)
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.
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: 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.
Continuity mistake: When Raphael knocks down Casey Jones and enables the purse snatchers to escape, they are getting up off the ground and running away. In the next shot, they are again seen getting up off the ground and running away.
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)
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)
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)
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)
Audio problem: In the Italian dub, Chief Sterns reads Mr. Pennington's number as 555-5219 instead of 555-5214. (00:28:30)
Continuity mistake: At the beginning of the movie, the stolen wallet ends up in Danny Pennington's hand who is tasked to hold it out for the ninja to grab it. In close-up Danny's hand is positioned below the sleeve of his T-shirt, in the shots before and after his hand is higher, between the sleeve and his body. (00:01:15)
Revealing mistake: In the opening of the movie, a citizen is reading his copy of the New York Post and you can actually read the date; Wednesday September 12, 1990. It is obviously a movie prop though, because the scene was shot in late 1989. How can you tell? Easy; he is reading it next to a newsstand kiosk full of magazines from that period; instantly recognizable are Vanity Fair's November 1989 issue with Baryshnikov on the cover, and GQ from December 1989 with Sting sporting an epic 'stache. (00:00:50)
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.