Continuity mistake: When the Turtles first arrive on screen behind Keno, they leap over the boy to attack the thieves. Their order from left to right when they walk up is Mikey, Leo, Donny, then Raph. The very next shot shows them in the air, and the order is now Mikey, Donny, Leo, then Raph. Donny and Leo switched places between shots. (00:03:35)
Continuity mistake: When Keno is trying to join the Foot Clan and is kick boxing with someone, the man in the background who is watching them, to see who is eligible to join, is standing cross-armed. In the next cut his arms are down by his side, and then cross-armed again. (00:43:30)
Continuity mistake: When April arrives at her apartment, she places down a folder like object, and then puts some paper and her keys on them. Next she places her purse on top of the left side of the objects. Moments later, after she goes upstairs, the Turtles come in through the window next to the stuff she sat down. Now the purse is on top of the right side of the items, and the strap is in a different position. (00:08:40 - 00:09:25)
Continuity mistake: When the turtles are watching April interview Prof. Jordon Perry on TV, Leonardo throws the TV Guide, which lands on the table behind Michelangelo with nothing on it. After Raphael complains about Michelangelo chewing the candy bar loudly, he stands up and not only has the TV Guide changed positions, it's now lying on top of another dark object that wasn't there before. (00:16:40 - 00:17:15)
Continuity mistake: The Ooze canisters look completely different from the first movie. The canister in Splinter's flashback was the same shape but had a different label, marked "Radioactive Material" with black and yellow bars. In this movie the canisters had a plain TGRI printed in black. Also Splinter refers to the canister as being broken in half, but in his flashback it is intact.
Continuity mistake: The Turtles are looking at the computer in the TGRI lab. The Foot Clan sneaks into the room just as the computer shuts down. Michaelangelo's bandana has both ends behind his head, but they are already in front of his shoulders in the reverse shot before he turns. (00:26:00)
Continuity mistake: Michaelangelo does his "Wax on, wax off" little gag. Notice on the counter two buckets. The metal bucket has no rags in it...except, it does when April arrives and Mike grabs the buckets, dragging that rag back. (00:20:50)
Continuity mistake: In the sequence with Michelangelo doing tricks with the yo-yo, whenever Donatello is visible in the background he's delivering a spin kick to the same enemy. (00:05:20)
Continuity mistake: Raphael dunks Keno into the laundry cart. Keno pulls himself up; between the Costume Designer and the Music composer credits 5 seconds pass but during the cut on Raphael kicking butt nearby the sheets he's on top of shifted a lot. (00:04:45)
Continuity mistake: Keno strikes a cool pose after downing three opponents at the beginning of the mall scene. As it cuts to a closer angler, the pose obviously changed; his shirt appears poofier and bares a huge part of his black undershirt. (00:03:40)
Continuity mistake: Keno stops his motorbike in front of April O'Neil's address. The passersby don't transition from the first shot to the second. (00:02:45)
Continuity mistake: Watch when Keno puts the pizza box inside the bike's trunk as he bodyshames the unimpressed girls; the tape that seals the box is loose and partially damaged. It's nicely flat and whole when he opens the trunk in front of her home, and with a different shape at its end when he shouts at the robbers raiding the mall. (00:02:15 - 00:02:50)
Continuity mistake: The broken donut looks different in Rahzar's palm from the close-up to the moment before the fight begins. (01:08:10)
Continuity mistake: In the first phase of the final showdown with the monsters, Shredder calls them to battle shouting "Tokka! Rahzar! Let the games begin." Midway through his shout-out there's a cut, and the Ooze canister is tilted differently. (01:06:30)
Continuity mistake: Once Chief Sterns has delivered his off-the-record speech about his off-the-record record, April chases him around to actually get something off him; in the background you can easily tell by the sudden shift in sunlight on the store signs and tents that time has passed between the two shots. (01:00:30)
Continuity mistake: When Raphael is captured, the Foot soldiers hold him in front of Tatsu, and then Shredder. The side of his head receives direct sunlight or not depending on the camera angle. (00:46:50)
Continuity mistake: April runs inside her office to get the call. Her boss angrily says "She's busy with her news manager" etc.; to the right side of the screen, notice a man in a pale blue shirt and beige pants. April in the next shot picks up the receiver and says "Donny?"; in the background, that extra is only now walking to the desk he was previously standing in front of. (00:38:15)
Chosen answer: He had moved away - he says in the third movie. We are never told as to where it was he moved to though.