Revealing mistake: When three of the turtles are playing Trivial Pursuit and Leonardo runs in to announce Splinter is alive, you can see a wire coming out of Raphael's shell. I guess it's for the animatronic head, but it's visible. (00:59:30)
Revealing mistake: As Michelangelo is waiting for the pizza guy, Donatelo cames through the sewer on a skateboard. A view of his feet is shown and his hands swipe across the screen. One of the times they come through his hand is not that of a turtle, but a human hand. (00:09:20)
Revealing mistake: In the scene where the turtles are leaving April's home and stop at the door to say hello before leaving, you can see Leonardo's sword handle bend like rubber, which it in fact is. (00:27:10)
Revealing mistake: In the scene close to the end when the turtles are fighting the foot soldiers on the fire escape (directly before the scene where Mikey ducks under the foot soldier's axe), Raphael thumps a foot soldier on top of his head and then rams the soldier's head into the stairwell. The only problem is the soldier's head misses the stair by about a mile. The sound effect of impact is there and the soldier even holds his head as if he were hurt. (01:17:20)
Revealing mistake: In the scene where Raphael is thrown through April's skylight after being attacked by a few dozen members of the Foot, the other Turtles and April check on him. As Donatello and Leonardo look him over, they lean on his shell, bending it with great ease even though a turtle's shell is supposed to be almost as hard as rock.
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: 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.
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)
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.
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)
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)
Revealing mistake: In the middle of the fight inside April's apartment, there's a comedy/action bit with Leonardo repeatedly trying to slash at a Foot Clan soldier. Ultimately, he fools him and kicks him. Behind him, another two bad guys arrive, but there's a very awkward bit in the choreography where one of the guys quite literally does not know where to go and puts himself in a corner with nobody there, stumbling into the other. (00:43:30)
Revealing mistake: Shredder is enraged because April O'Neil mentioned the Foot clan. He throws a knife at the screen, with an effect that is not only transparent in how fake it is, but shows cracks with secondary circular holes like it was sprayed with bullets. (00:18:05)
Revealing mistake: When Raph trips the two purse snatchers, the second one doesn't come anywhere near connecting with his leg. (00:11:40)
Revealing mistake: During the fight sequence in April's apartment, two foot soldiers dunk Donatello into a fish aquarium. Instead, you can see how it's actually a steel tub full of water into which he's dunked (fullscreen). (00:43:10)
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.