Continuity mistake: Frasier and Roz are in the Cafe talking about the dating service - Roz is holding her mug by its side in her right hand - it switches from her holding it by the side to holding it by the handle and from one hand to the other several times during the scene.
Revealing mistake: 4 minutes into the show, Frasier gets off the elevator and goes to an office door with keys to open it, he tries the keys and they don't work. He realizes he missed his floor. A woman opens the door and they start talking about a dating service which he says he doesn't need, and he pushes the elevator down button, which lights up. The doors open and a man gets off. It's going up, which he finds out from an ex-girlfriend on the elevator. The down button light goes out before he gets on to go up with her. The light should only have gone off on the way back down.
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Continuity mistake: The scene where Charlotte comes to Frasier in the restaurant to tell Frasier his date has cancelled is poorly edited between shots. Watch the folder once she has pulled it out: in almost every shot, the side facing the camera changes, and when Charlotte gets up, it disappears completely.