Revealing mistake: In "Not Normal" when SpongeBob says "Hmm. This video tape should help," his left arm is missing. (00:01:25)
From Method to Madness - S3-E18
Revealing mistake: After the fight between Stewie and Olivia at the concert hall (followed by their breakup), Simon tells Stewie that the act without Olivia is "over" as he turns to walk off the screen. However, before Simon is even partially out of the shot, he completely disappears. (00:18:45)
A Bicyclops Built for Two - S2-E13
Revealing mistake: At the end of the wooing near the end, you can see that Fry has four arms.
The Dark Network of Etemon - S1-E15
Revealing mistake: Watch the scene where Biyomon and Palmon are eating. A Pagumon passes, Biyomon turns her head and then has two beaks. Obviously a frame overlap.