Continuity mistake: Late in the show, Frasier throws his notebook on the coffee table and it lies flat near the books. A couple of shots later, it is on top of one of the books, with pages flipped back. No one went near it in the meantime.
Continuity mistake: During the scene where Daphne is upset because there's a spot on her dress, Roz is standing with her arms by her sides - then in a quick shot change, her arms and hands are up in front of her, holding her purse and wrap.
Continuity mistake: At the start of the show Niles is playing the piano. He turns to talk to Frasier and his hands are in his lap, but in the next shot one hand is back up on the piano keys, with no time for this to have happened naturally.