Deliberate mistake: When the turtles and April escape the building filling up with water, the shot where the hall is filling up with water is used twice.
Revealing mistake: When Donnie is fighting some foot clan solders, his belt has an M on it for a frame.
Revealing mistake: When the channel 6 crew member is telling April they should go, his hand disappears for a frame.
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.
Continuity mistake: When Bebop's gun is sliced, Raph comes in from the left to knock him out. When he's down, Raph disappears.
Continuity mistake: When Leonardo slices Bebop's gun, he's wearing red.
Invasion of the Punk Frogs - S2-E8
Plot hole: Shredder meets the frogs for the first time and gives them clothes using the holographic projector. The frogs continue to wear the same clothes for the rest of the episode, even without Shredder being around.
Continuity mistake: The turtle van falls on a bridge, the turtles escape swimming. Shortly afterwards, April appears driving the van, looking for the turtles.
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.