Deliberate mistake: When Marge goes offroading to get home there is a grassy field which leads right up into the Simpson driveway. However, in all other episodes there is no grassy field and instead there is a house in the spot where the field would be.Tobin OReilly
Continuity mistake: When the person delivers the animation cell, his skin changes from white, to brown and then back to white. When Bart looks through the letterbox to see who was there, his skin is white. When he gives the box to Bart, it is brown. When he hits Bart in the face and says "that's for keeping me waiting", it is white again.
Continuity mistake: John is wearing Homer's old "Pin-pals" bowling shirt when the Simpsons first meet him, but only after we see the back of the shirt does the name "Homer" appear over John's breast-pocket; clearly there was nothing there during their entire previous conversation. And even if this is a deliberate "mistake" for comic purposes, in 7th season episode"Team Homer", the very same bowling shirt is ripped to shreds when Homer is being mauled by Mr.Burns' dogs at the very end.