The Catwoman from Channel Six - S2-E12
Other mistake: When Irma finds April's Turtlecom and fortuitously contacts the Turtles, Leo answers the call and holds up the communicator in his right hand. The problem is that in the close-ups of Leo's open communicator, the animation of his wrist area is not complete, so his hand looks disembodied. Additionally, after Leonardo answers the Turtlecom call from Irma, she asks, "Who are you?" and in the next shot of the Turtlecom Irma is holding up, we see Raphael moving his lips as he says, "I'm Leonardo."
The Catwoman from Channel Six - S2-E12
Continuity mistake: Shredder thinks, "Those idiots have learned their lesson," so he transports Bebop and Rocksteady back to his lair. Bebop's wristwear switches to opposite sides; the chain bracelet is now on his right wrist, and the studded wristband is on his left wrist, then both return to their proper wrists. This happens again when Shredder makes the crack about his cheap mutant labor.
The Catwoman from Channel Six - S2-E12
Continuity mistake: When Shredder uses the matter transporter to send Bebop and Rocksteady to the city dump, Bebop's black bandoleer vanishes and reappears; then it happens again and again in the following shots.
The Catwoman from Channel Six - S2-E12
Continuity mistake: After the beloved TV is destroyed during the fight at the sewer lair, when Rocksteady attempts to help Bebop he's stopped by Mikey, but as Rocksteady smashes into the wall, his bandoleer and other strap have switched to opposite sides, then revert to their proper positions.
The Catwoman from Channel Six - S2-E12
Continuity mistake: When Leonardo cuts off April's collar, she asks what happened, but instead of it being Leonardo standing there with the sword, it's Donatello with the sword.
Other mistake: The turtles are racing to save April, who is kidnapped by Shredder, and trying to get to the roof. They run into a squad of the royal guards and one of the guards shouts: "Halt! Hands in the air or we'll open fire!" Now, I would like to see that because every one of the guards is holding a sword. (00:14:00)
20,000 Leaks Under the City - S3-E14
Continuity mistake: The Octopus grabs Rocksteady, in the next shot on the boat, Bebop disappears and Rocksteady is on the boat.
Michelangelo's Birthday - S3-E31
Factual error: The very beginning of the episode shows Michelangelo's Birthday circled on the calendar, and it is shown as the second Tuesday of the month as well as being the 13th day. The second Tuesday of a month can never be the 13th. The earliest the 13th of a month can be is the second Thursday.
Suggested correction: This is simply wrong. If a month starts on a Thursday, the first Tuesday will be the 6th, and the second will be the 13th.
Slash: The Evil Turtle from Dimension X - S4-E33
Continuity mistake: Pizzas keep reappearing on the counter as Slash eats them.
Adventures in Turtle-Sitting - S6-E4
Revealing mistake: When Leonardo throws his katana at the tree which Michelangelo and April are tied around, you can see the rope is cut and begins falling off the tree before the katana touches it. (00:20:33)
Continuity mistake: Shredder's hand blades temporarily disappear when he's talking to Krang in the Technodrome.