Continuity mistake: Frasier is reading the newspaper while Eddie stares at him. He picks up his coffee and we can see he's reading the back page of the newspaper, but from the angle over his shoulder he is reading the front page. It goes back to him reading the back page as he says "you will not distract me" to Eddie.
Continuity mistake: Marty and Sherry are looking at old photos to use at Marty's birthday party - we can see one in Sherry's hand that has noticeable brown marks down the back, as though it had been glued in an album. The next shot shows Marty passing this one to her, even though in the shot before it was in her hand. When Sherry passes the picture over to Niles and Frasier, in the shot when they get it, it's not the same photo, as it is clean on the back.
Visible crew/equipment: When Frasier and Daphne are sitting talking in the sitting room, Frasier stands and the camera angle shows the fake wall above the fireplace - you can see the flue and that the wall stops just over where the shot normally finishes. There is visibly no proper wall behind the fireplace, you can see clear through to the construction behind.