Continuity mistake: There was an episode in which Martin attempts to end a feud between Frasier and Niles by telling a story about his detective partner. He starts with the line, "I never had a brother...", but in the episode about Frasier's cousin Nikos getting married, Martin's brother Walt was introduced.
Continuity mistake: As Frasier and Niles are starting work on their book, Marty gets four snacks and a beer and sits down in his chair. He gets up and we see the two bags that were behind the beer and can of something are now in front of them. Marty never touched them during that time.