An executive producer of The Simpsons, Matt Selman, has tweeted about this incredible error in a classic and well-known episode of the show. Look at the background.
In an episode set before Maggie was born, a picture of her can be seen hanging on a wall in Homer and Marge’s house.
When the error was pointed out by Selman, The Simpsons' Al Jean responded with this. Fans chipped in as well.
What is so interesting about this continuity error is that this is the classic episode of The Simpsons where Lisa asks Homer why there are no pictures of Maggie in the family photo album. Homer then tells a story of his unhappiness when he first learned that Marge was pregnant with her.
Homer had just quit his job at the nuclear power plant to work at a bowling alley, but then after hearing the news, he had to ask for his job back. Mr Burns then did this:
The scene directly after the background error is the scene where we see Maggie being born. Homer, who was until then very vocal about not being keen on having a third child, totally changed his view upon meeting her for the first time.
Leading to this incredibly touching final scene — probably one of the most moving in the show's history.
Turns out that there were photos of Maggie up all along.
UPDATE: To anyone who might think that the photo showed a baby Lisa and not Maggie, this isn’t the case. In any scene in which Lisa appears as a baby, she always wears her white necklace.
Oh and if you’ve seen this still of Homer with hair holding a baby and assumed it’s Lisa, that’s wrong too.
Further investigation confirms the person with hair is actually Herb, Homer's long-lost brother. And he was holding Maggie, not Lisa.