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.
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.
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.