Continuity mistake: When Shredder unbalances Donatello in the fight his left foot is close but not inside the large shadow area, but Michelangelo attacks him right away and despite his lack of movement, now that foot is in the shadow cone. (01:20:20)
Continuity mistake: The Turtles are making fun of The Shredder's name once he announced it. Look at Michelangelo when he recites the coleslaw joke; his bandanna goes down the right side of his back, but it's on the left side in the next shot. (01:19:05)
Continuity mistake: When the Turtles strike a pose after they wasted all the Foot soldiers before their big showdown with The Shredder, the ninja lie unconscious at their feet in different position. Even the roof is lit differently. (01:18:20)
Other mistake: Danny (who somehow knows where the Turtles hideout is, maybe someone else in the Foot clan told him) is hiding in the closet, cowering in fear in a corner of it. April, who is way behind and with her view even further obstructed by Leo and the others as she steps to the left, guesses that it is him even if the little guy hasn't spoken a word yet. (01:03:45)
Other mistake: April mentions that she has not been to the old farmhouse in years, and that the nearest neighbour is four miles away, but the morning of their departure is signaled by a rooster crow. (00:51:00 - 01:01:50)
Continuity mistake: Master Tatsu is raging against the students, and slams one against the lockers. Another Foot soldier tries to restrain him. The unmasked victim of the assault is clutching the shoulder bit of Tatsu's hood, but his hand is further down his arm in the reverse shot. (00:49:00)
Continuity mistake: In the rumble inside the antique store, Mike at one point squeals that they could use Raph, "right about now." Cut to Donatello fighting some bad guys to the left of an unimpressed and passive Master Tatsu. The following shot has Don fighting Foot clan members to Tatsu's right, and it's Leonardo to be battling to Tatsu's left (right side of the screen). (00:45:30)
Continuity mistake: Mike thanks to Don's help does the "Wheel of Fortune, dude!" move; the floor next to him is relatively clear from debris and he sweeps it, but when the bad guy throws a single axe strike next to his head, the floor is all messed up and cut. (00:44:00)
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)
Continuity mistake: In the rooftop fight, as Raphael quips about the Foot guys studying the abridged version of the Ninja book of fighting, you can see his belt is hanging kinda low, at the hips almost. In the next shot, Raph is fighting with his belt in senior citizen mode, pulled all the way up to 2/3 of the torso. You can tell quite easily because being a turtle his belly is divided in sections. (00:40:45)
Other mistake: In a close-up of Chief Sterns' desk as he calls the parents of the juvis, you can see (top right) that Danny's arrest date is 9/3/89, which is inconsistent with the date established at the beginning. (00:28:20)
Continuity mistake: April is laughing at Mike doing a Rocky impression. Camera behind her shoulder; notice her hand slips off the table. Back to a frontal view, and her hand rests on the table as it was before. (00:26:10)
Continuity mistake: When April tries to rationalize what she's seeing, says pointing at the Turtles; "And you guys.. " Mike and Leo are looking at her. Leo's arms are low, but in the reverse shot they are held higher towards her. (00:22:25)
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)
Other mistake: In the Italian dub, when Michelangelo hangs the telephone reminding the pizza delivery people that "The clock is ticking, dude!" the translation says "Your days are numbered", which is obviously incorrect (the clock is ticking on the pizza delivery time; the guy will be two minutes late). (00:08:05)
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)
Continuity mistake: Right after Donatello busts through the barn doors with an old Ford truck, its hood closes by itself between shots. (00:53:10)
Revealing mistake: After Splinter releases the nunchaku from Shredder's spear, he falls from the building's ledge. But notice how Shredder stops abruptly right before the series of shots which show him taking the long fall into a trash compactor, indicating that he actually lands on a mat. (01:23:00)
Continuity mistake: While driving Danny to school, Charles' left hand grips the steering wheel. But in the following shot where Danny opens the door to run away, his left hand is resting near the window sill instead. (00:30:25)
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.