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 Ringer - S1-E1
Revealing mistake: After crashing on his skeleton-drawn throne, Ganon stands up and orders the remaining 3 skeletons to attack Link and Zelda. Watch his head as they pass by him. At two different times while they pass by, Ganon's head randomly jumps out of place and onto his shoulder for a frame or two, then back where it goes. (00:12:30)
Robo Koopa - S1-E52
Revealing mistake: When Bunsun walks up to Dr. Nerdnik to free him, an animation mistake is noticable. Bunsun is far away and she walks up to him, and during this whole sequence her body is in front of Dr. Nerdnik, according to the camera's view. (00:04:55)
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)