Continuity mistake: Towards the end of the show, Frasier is explaining to Niles how he was stood up that evening; at the same time he is getting himself a glass of sherry. Niles says, "there was no emergency", we see Frasier repeat the actions to get a glass of sherry all over again.
Continuity mistake: After Frasier watches the video of Eddie, he tosses the remote on the coffee table. When Niles comes in a short time later, the remote has disappeared, but when Niles asks, "Aren't you going to ask me what's up?" we can see the remote again, on top of the manila envelope. It disappears and reappears throughout the scene.