Best Day Ever/The Gift of Gum - S4-E20
Revealing mistake: When Squidward says "I suppose if you haven't fixed my clarinet, the concert would have been a bust", Sandy's tail is the same color as her suit.
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)
Revealing mistake: When someone suggests crying as a way to get the emperor out of Fry's body, he says 'that's a great idea', the emperor's face stays still on Fry's stomach, instead of moving in sync with Fry's body. (00:15:50)
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.