Chitty Chitty Death Bang - S1-E3
Continuity mistake: In the flashback of Lois making a birthday cake, the cake has dark pink icing on the top and light pink icing on the sides. When Peter comes in to talk to Lois, the two colors have reversed. (00:01:35)
Continuity mistake: When Fry is queueing for the booth, he opens the piece of paper, showing the picture and writing. Just before he steps in to the booth, it's changed colour and gone blank, then in the next shot it's back as before. (00:07:45)
Your Shoe's Untied / Squid's Day Off - S2-E2
Character mistake: In "Squid's Day Off", a wide shot shows Mr. Krabs exiting the hospital, except the building says" ENEREENCY" instead of "EMERGENCY."