Shredder's trousers disappear when he is the scene kneeling and controlling the robot spider.
In the beginning when Shredder and Baxter are seen by the turtles on top of the World Trade Center, the towers are evenly parallel to each other. The towers in real life weren't evenly parallel. Instead they were diagonally next each other.
Just as the glider portion of the turtle blimp is about to hit the ground after Baxter shoots the turtles down, the stop light seen has the green light on the top and the red light on the bottom instead of the red on the top and green on the bottom.
When Michelangelo says "You said a mouthful.", his mouth moves, but Donatello's voice is heard instead of Michelangelo's voice.