In the scene where Frasier, Lilith and Niles are analyzing the reasons for the previous night's events. Frasier is sitting near the door and gets up to walk across the room. You can clearly see he has his shoes on but when he sits down on the sofa on the other side of the room where his clothes are, he is next seen putting his shoes on.
Niles rubs his right cheek to warm it. But it was his left cheek against the ice tray.
Soon after Frasier leaves Lilith in the control room to go to a meeting, Roz comes in and starts talking to Lilith. While she is talking, she holds onto the control room door and actually sticks her fingers through the door window. The glass has obviously been removed to eliminate glare from the stage lights.
Earlier in the season, with the episode titled "The Kid", Frasier sarcastically tells Roz, "Oh, that's right you've never met Lilith have you?" during his attempt at assuring her that Roz well indeed make a good single parent. But in fact Roz does know Lilith, they just haven't shared a scene together until this episode.
When Frasier shows up at Lilith's hotel room (with Niles in her bed) and she yells "It's Frasier!", Bebe Neuwirth mispronounces Frasier's name as "Fray-zer."
Lilith and Niles conclude that their sexual encounter cured his narcolepsy. Yet he had two narcoleptic episodes the morning after the sex.
When Lilith says her dress is from a couture line called "Encore", Frasier responds "Bravo"! With his vast knowledge and experience of musical performances, he would know that "Brava" is the correct word when applauding a woman.