Revealing mistake: Carl, Eddie, and Steve are out ice fishing. At one point Carl falls through the "ice" and you can clearly see that the "ice" is made of some sort of styrofoam. It looks like the stuff used for packaging. The snow looks just as fake.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: After Homer brings Santa's Little Helper home, Homer and Marge hug, and if you look behind them, the background is upside down. There is a picture hanging upside down, and there is a lamp which seems to be hanging from the ceiling. Then in the next shot, the background is normal. (00:21:40)
The Library - S1-E3
Revealing mistake: In the extra 'Library' scene, the book that Bean is given already has the loose pages before he has been at them with the knife. (At one point the pages get pushed forward a little bit, meaning that they're not fastened into the book.)
Save the Max - S2-E3
Revealing mistake: When they are reading the reviews in the newspaper, look at the back page. It's the sports section. Next when Jessie comes back to Zack and tells him what Mr Belding was hiding, she says the paper is from 1968. But look at the back of that paper also. They are using the exact same paper. The reviews and the 1968 paper are the exact same.
Shanpû no hangeki! Hissatsu shiatsuken wa mimo kokomo ubau - S1-E16
Revealing mistake: In his close-up when he grins at Ranma after his request to help him figure out what happened to Akane, Ryoga is drawn really obviously with the hair going under his eyebrows. (00:15:00)