Plot hole: Niles makes up Frasier's couch to sleep in and when he lies down he lets out a yelp - and pulls a plastic pirate's hook from behind the cushions. Earlier Niles had appeared wearing a pirate's costume but at no point did he have a hook, nor did he go near the couch. His overcoat had been on the floor the whole time so it couldn't have come from there. It would have been difficult for it to get behind the cushions unless deliberately shoved there, which we never saw and makes no sense anyway.
Continuity mistake: At the beginning of the show, Niles, Frasier and Daphne are at Cafe Nervosa. Daphne is standing up talking to Eric the server and Niles gets agitated, and spills sugar everywhere. Eric throws down a dish towel so they can clean it up. The dish towel appears and disappears several times during the scene.
Plot hole: Niles phones Frasier to tell him Daphne is staying at his place because of the storm. Frasier's phone is in its usual place on the room divider/bookcase behind Marty's chair. After Frasier and Marty leave to rescue Daphne, Niles phones again and Eddie is standing up on a chair staring at the phone. Only problem is, the phone is over on Frasier's desk, where there normally is no phone. If he did have a phone there, it is only a few feet from the other one, which makes no sense.