Revealing mistakes: In the episode with Raymond's diary, Marie makes like she is reading from Raymond's diary, however from the angle that she's holding it, it's obvious that there's no writing on the page except for a standard header on every page. Raymond also doesn't write anything when she asks him to amend the entry.
Continuity: In one of the episodes, Raymond is talking to Debra. If you look at Ray's shirt, it is clean. Next shot, it is dirty. It keeps doing this.
Continuity: Robert is supposed to have a quirk where he touches food to his chin before eating it. Throughout the shows, he sometimes does this and sometimes doesn't. He mainly does it in the episode it it mentioned in.
Errors made by characters (possibly deliberate errors by the filmmakers): In one particular episode, one of the actors accidentally refers to Doug Heffernan (of King of Queens, as played by Kevin James) as "Kevin" - his real life name.