Revealing mistake: When Frasier comes into the chalet after skiing he doesn't show any of the visible effects after a hard day on the slopes. Meaning, his face isn't even flushed from the cold, his hair is perfectly combed after wearing a hat and there is not even a drop of snow on his boots.
Plot hole: At closing time, Cliff, Norm and Woody spontaneously decide to go to Cliff's house. Sam then enters the bar after his date at Melville's. Later in the scene, Rebecca asks Sam about the 'Three Stooges', to which Sam sarcastically replies that they went to Cliff's house. But how could he possibly know that since he entered the scene after they had already left.
Other mistake: Right after Sam tells Carla he will sleep with the next woman who walks through the door, in the background there is an "Extra" (blonde-haired woman seen in background between Sam and Carla) who starts to cross right then turns and crosses lefts then turns right and stops and looks confused as to where she is to cross. Obviously she was given directions of which way to cross and when, but forgot.
Continuity mistake: Just before they reveal the answers of Final Jeopardy, they take a wide shot, and Cliff's question (Who are 3 people who have never been in my kitchen) is already revealed. But when they take a tight shot and ask Cliff to reveal his question, it is covered up.
Character mistake: Cliff tests Norm's memory by asking him who the bad guy in 'Herbie The Love Bug' was (presumably meaning the first movie, which was just 'The Love Bug, ' no Herbie in the title, and not the TV series that actually had the 'Herbie, the Love Bug' title). Norm answers Keenan Wynn, and is told by Cliff that is correct and that his memory is OK. Wynn was the antagonist in the second movie, 'Herbie Rides Again' (reprising his role from the 'Absent-Minded Professor'). The bad guy in 'The Love Bug' was played by David Tomlinson of 'Mary Poppins' fame.