Factual error: When they first assault the city, the Greeks construct catapults. Only problem: catapults were invented at 400 - 300 BC, i.e. about 800 years later; and the first models looked similar to giant crossbows. The one-armed onager and similar types (as seen here) were a later Roman invention.
Continuity mistake: Episode 1-22, Kansas v. Tom's Parents. In the opening sequence where Tom and Susan is attending a party, watch the glasses and their contents. In some shots Tom is holding one glass in his left hand, in other shots he's holding it in his right. In another shot he's holding two glasses. The number of olives in the glasses also changes between shots.hannisen
Plot hole: In their previous encounters with the Triceratons, the Turtles had to learn the hard way that the Triceratons breathe not oxygen but a combination of nitrogen and sulfur, which is detrimental to most Earth lifeforms, and thus had to wear special rebreathers. When the Turtles, Splinter, April and Casey enter Zanramon's throne room along with Traximus, none of them wear any breathing equipment to protect themselves from the hostile atmosphere.Daniel4646
Continuity mistake: Jamie and Adam are shooting at Police badges to see which one would potentially stop a bullet. When they get to the third badge, it is held up to the camera. It says 'Jamie Hyneman' on the badge. The badge is then shot, and shown again to the camera. This time the engraved writing on the badge has changed to 'Adam Savage'.Mr Manchester
Continuity mistake: When Adam gets angry at Joan in the art room because of the camera, his half-made sculpture is sitting on the desk. When he grabs his bag toward the end of the scene, he accidentally knocks it over, unbalancing it. But in the next shot it's balanced again, then suddenly it's unbalanced. This happens several times between shots, and can even be seen in one shot before he knocks it over.