In April's apartment, after the turtles watch April's interview on TV in which she thanks Raphael for saving her, Donatello says that Raphael is turning red from embarrassment, but Raphael actually responds in Leonardo's voice, not his own.
During the final fight, a foot soldier is thrown into the staircase of a fire escape. He grabs his head in pain and we hear the clanging sound, but we see that his head never even got within a foot of the metal.
Towards the beginning of the movie when the young kids are bringing stolen goods to the foot soldiers in the large cargo van, the foot soldiers close the double doors at the back of the van and the sound of the doors latching is nowhere close to the time that the doors actually close.
The exact same sound effect (a metallic "rub") is used both when Shredder turns towards Danny after his speech, and when he lifts his spike to Splinter's neck to threaten him- yet they are two completely different actions, and the first instance doesn't even warrant the sound effect in the first place.
When Danny exits the sewer via the manhole cover, he slides it up and to the left. When the scene cuts to Casey Jones and then Casey Jones walking passed the manhole cover, it is noticeably down and to the left.
When Raphael is looking at the traffic from the top of April's building right before the foot come at him, the building looks like it has at least 15-20 stories. When Danny is looking at the building burning it has only 2 stories.
While in the ground floor of the junk shop during the battle with the Foot Clan, Leonardo is seen helping April uncover an escape route. Then Leonardo is seen fending off the Foot in the background. The following shot shows Leonardo back in the same place at April's side.
When Donatello is skateboarding in the sewers to meet with Michelangelo while Mikey is waiting for the pizza, you can see, for a couple of frames, a human hand (which should be Donny's) move in and then out of the camera viewpoint while he is doing a spin.
Shortly after Casey is seen chopping vegetables with a sword, there is a shot of all of the turtles gathered in one room. In the bottom center of the screen, you can see a mic cord coming out of the bottom of a turtle's shell and going down his left leg. This is Leonardo. Behind him, another more visible cord can be seen coming out of the left side of Raphael's shell.
Endorsement backfire: Because the turtles have long been devotees of pizza, Pizza Hut was one of the main endorsers of the movie, creating and distributing much of the Turtles' merchandising before the movie's premiere. However, all the deliveries in the movie were shown to be from Domino's.
When Raphael gets attacked by the Foot soldiers on April's roof, one of them tosses both of his sai over the edge of the building. Yet later in the movie, he has the weapons back even though he never had a chance to find and recover them.
At the beginning of the "This is What we Do" sequence, when the camera is focused on the cigar-smoking boy playing pool, the Bubblegum Girl from the very next shot can be seen waiting around on her mark in the background.
Right after Raphael is dropped through the skylights, he comes crashing to the ground. His brothers run to his side. As they do this you can see Donatello touch Raphael's shell. When he does this you can see the shell move inward as if it is something soft like foam.