Continuity mistake: In the beginning scene, Niles and Frasier are arguing by the door. Right after Niles leaves and Frasier yells "Get out! ", the camera pans out and you can see the entire room, at which point Roz is holding her wine glass in her right hand. Immediately after, the camera cuts to Roz who says, "yeah, some nerve..., " and the glass is now on the table in front of her left hand. There wasn't time for her to set it down (especially across her body), and the camera stays focused on her continuously through both shots.
Continuity mistake: Daphne visits the radio station where Frasier works about halfway through the episode. She holds the earphone piece up to her right ear, then it cuts to a different camera angle and the headphones are lying on the desk with no time between shots. It's actually quite glaring.
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Continuity mistake: In the episode "Call Me Irresponsible" from season 1, Frasier and Catherine are making out on Martin's old chair, which starts vibrating (probably because they inadvertently hit a switch on the side). But in "Give Him the Chair", Frasier tries to replace Martin's old chair by buying a new one which has a built-in massager. When Martin tries it, he looks horrified and says "That's disgusting", even though his beloved chair had the same feature.
Plot hole: When Frasier is trying to get to the bottom of Niles' problem viewing Daphne in a real way, we see them both against past scenes in the show; Frasier watches and comments on some of them as he talks but because he is actually only discussing these events with Niles, he shouldn't be able to see a visual of anything such as the dress Daphne is wearing during the dance scene.