Continuity mistake: When Niles is engaged in his ironing fiasco, Eddie is watching his every move. When Niles heads to the kitchen to get spot remover, Eddie is sitting on the footstool. The next shot shows Eddie turned to watch Niles - but he is now in the chair; it is not just a tricky angle, as he actually lays his chin on the back of the chair. There was no time for Eddie to jump from the footstool to the chair.
Continuity mistake: At the end of the show, when Martin, Niles, and Frasier are leaving Niles's place to go out for ice cream, they leave Maris's opened package on a large footstool next to a decorative metal bowl. When they return (closing credits) with their ice cream the package and its wrappings are gone - even though no one was left behind in the apartment.
Continuity mistake: Frasier, Niles, Daphne, Marty, and Abby are having dinner at a restaurant. Abby has a notepad and cellphone on the table. When Niles announces Donny has just walked in, the next shot shows Abby drinking champagne, but the notepad and cellphone have disappeared.
Continuity mistake: Simon has shown up at Daphne's shower and is standing at the bar/table with Roz and Holly. There is a bottle of champagne on the table, next to an ice bucket - but when Daphne drags Simon away the shot shows that the bottle has mysteriously made its way into the ice bucket.
Continuity mistake: Roz is talking about having a fling - while she takes the notebook, which was open on the coffee table, shuts it under its own weight. She keeps talking and waving her hands around, and in the next shot the notebook is open again, even though she didn't touch it.