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.
Continuity mistake: In this scene, Martin and Daphne are arguing about Martin buying the gift basket for Daphne because Daphne knitted the sweater for Martin. Daphne says the basket cost too much, so Martin begins to take items from the basket and put them on the table. Then as the argument progresses Martin and Daphne decide to take back their gifts. Martin places the gift basket on his chair (the two items that were taken from the basket are still on the table) and Daphne takes the sweater. A minute later they make up and agree to re-exchange the gifts. Daphne gives Martin his sweater and when Martin reaches for the basket, all items are there, including the ones that were still sitting on the table when he put the basket on the chair.
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.