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)
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)
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)
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)
Other mistake: After Michaelangelo hums to agree with Donatello's comment moments after Casey & April have finished arguing and slamming doors, you can hear Michaelangelo humming "Old MacDonald," but you can see a shoulder strap and a purple headband indicating this is Donatello. (00:52:15)
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: In the music within the ending credits, the lyrics incorrectly state that Raph is the leader of the group when all Turtle fans past and present know it is Leo.
Other mistake: After Leo's failed attempt of fighting Shredder for the first time, Mikey and Donnie then play Rock, Paper, Scissors to see who fights Shredder next. It then cuts to Casey talking to "The Foot" where you can hear Mikey fighting Shredder. The next scene shows all four Turtles in a huddle regrouping, breathing heavy, and out of breath. According to what we heard, Donatello shouldn't be out of breath as he has not fought Shredder for the first time yet.
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.