Pilot: The Spirit of Christmas (Jesus vs. Santa) - S1-E1
Revealing mistake: Each time Jesus turns his head to speak to the children when he is beating Santa Claus, he has two left arms.
The Wedding of Bobby Hill - S3-E14
Revealing mistake: During Rad's haircut from Luanne, there is a shot that shows the both of them in the mirror. You can see both their reflections and the room in the mirror but the objects on the counter in front of Rad have no reflection.
Revealing mistake: Right after TJ and friends are looking at the "thermometers" of cans, the Ashleys have at least 4 crates of cans that they bring in on forklifts. However, the end result is 4,362 cans for the Ashleys. This may seem kind of picky, but I think there was more cans than 4,362.
Magical Express Murder Case: File 3 - S2-E12
Revealing mistake: Akechi learns about Reiko Chikamiya's death from the newspaper. It's not a very respectful newspaper, since at first glance you can see in the body of the article a big "DUH." A column away, you can also read "he's the best running back in the X-league", which certainly the middle aged woman wasn't. (00:15:40)
Revealing mistake: In every episode, the windows in both the kitchen and living room areas never reveal any scenery outside them during the day or any reflections from the inside at night.