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.
He's Too Sexy for His Fat - S2-E17
Revealing mistake: During the scene when the people at the pool think Chris is a car sitting on the diving board, just before Lois moves out of the shot before the scene changes, her lips disappear for a split second. It's really fast but still easy to notice even without pausing or slow motion. (00:07:20)
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.