Continuity mistake: When Homer is first interviewed for 'Rock Bottom', the clock behind him stays at 5 O'Clock for the duration of the interview, but when the interview is actually shown on the TV, the times keep changing. The hands on the clock are also slightly different.
Continuity mistake: When we first see the medicine cabinet in the Simpson's bathroom the hinges are on the left. When Homer pokes it with the wire it opens as if the hinges are on the other side. The last time we see it, when Lisa rescues Maggie, the door is missing altogether.
Factual error: The Suburb of Wooloomooloo where the chase starts is in Sydney, and the Simpson family are chased all the way to the American Embassy which is in Canberra, a distance of at least 150 kilometres. That's some impressive running, especially for Homer.
Continuity mistake: This episode rewrites the entire backstory of Marge and Homer. For starters, Lisa and Bart were both not born yet, despite the fact that in the episode "Lisa's First Word," the '84 Summer Olympic games were being broadcast, and Bart and Lisa were both there. In this episode, Homer and Marge were just dating, but again in "Lisa's First Word," they were married and living in their Evergreen Terrace house. Additionally, Maggie was born in the episode "And Maggie Makes Three." Homer also lost all his hair in that episode, yet in this episode in the early 90's he still has a full head of hair.
Continuity mistake: Season 20, episode 16, "Eeny Teeny Maya Mo." As Marge is feeding Maggie a grapefruit, Bart takes out his bongo drums and plays them. Watch as Bart plays - the shot zooms in from the back of Bart towards Maggie, and you can't see Marge in the scene sitting close to Maggie; the next shot shows her though.