Character mistake: In the scene when Raphael crashes through the window, as April and Leo converse on his well being, you can see Donatello mishandling his bow staff on the left.
Suggested correction: You're going to have to define "mishandling" and explain how it's a mistake, because I watched the movie last night, and then just looked up the scene again on YouTube, and there's absolutely nothing wrong with what he's doing at the moment in question. Certainly nothing that would qualify it as a "mistake." He's just fumbling with his staff as he pulls it out and gets ready for potential combat, since, you know, his brother was just thrown in through a window. At best, he sort-of loses grip on his staff for a half-second before grabbing it again... but that's not really a "mistake." Fumbling with objects (especially in a high-stress situation) is something that happens to people in real-life literally all the time.
Character mistake: When Raphael is chasing Casey Jones after their fight he vaults over a taxi hood, never takes his eyes off Casey, but he somehow loses him.
Suggested correction: 2 things are happening; a shell backed stocky Raphael is chasing a lighter human athlete Casey. Casey has freedom of movement, whereas Raphael can't stray much from the shadows in hiding. :-) A knocked out Casey wouldn't be helping the Turtles out of the next evening with that memorable entry so I'm glad Raph lost the chase.