When Frasier and Martin prepare to play their final game, Frasier asks who should go first, and Martin replies that the person who lost the last game is supposed to start. However, according to the official rules of chess, the player with the white pieces always goes first.
In the opening scene, Niles confesses to feeling lonely, to which Daphne replies, "...perhaps all you need is a little company at the apartment." This is one of the few references made during season three to where Niles has been living since his separation from Maris.
In "The Last Time I Saw Maris," earlier in the season, Niles states that he has rented "a bachelor pad." There is also a brief reference by Niles to his "new address" in the episode "Come Lie With Me." We learn nothing more about where Niles lives until he rents an apartment at "The Montana" in season four's "To Kill a Talking Bird."
Martin : (Sees Niles' new dog) What the hell is that?
Niles: It's my dog, my new best friend.
Frasier : Yes, Niles saw her in the pet store and had this inexplicable attraction.
Martin: You can see her ribs.
Frasier : Hint number one.
Niles: Maris and I used to play chess every Thursday night. Oh, how she loved the game.
Frasier: No wonder. The king is stationary while the queen has all the power.
Daphne: How are you getting along, Dr. Crane?
Niles: Oh, all right, I guess.
Daphne: Feeling a bit lonely, are we?
Niles: Only sometimes when I'm by myself, or other times when I'm with other people.
Daphne: It may not be the place to say this, but perhaps all you need is a little company at the apartment - something warm and friendly to come home to?
Niles: Well, I'm sure Dad would miss you.
(Daphne laughs and bats Niles's arm)
Daphne: Oh, Dr. Crane.
(Niles laughs with her and bats himself in the arm)
Niles: Oh, me!
Martin: I don't see any reason why I should play you again.
Frasier: If you win, I'll give you five thousand dollars.
Martin: (jumps out of bed) Get outta my way.
Frasier: Oh, did I mention the cemetery called? Apparently they have to dig a sewer by your plot.
Frasier: No more Mr. Cordial guy.
Roz: Alright, I'll set Naj straight.
Frasier: Well, if you manage that then you really would have a story.
Roz: I have an appointment this afternoon with Naj.
Roz: He's the hottest hairstylist in Seattle.
Roz: I think he's getting a little bored with me. When he's cutting my hair, I can't even think of anything to say.
Frasier: Well, how's this for an icebreaker: say Naj, where'd you get such a stupid name?
Niles: It's absolutely breathtaking. I'm breathless. (chokes) I need to take a breath. (breathes in)
Frasier was similarly embarrassed by Woody at chess in the Cheers episode "Spellbound."
Niles: Oh yes, how is the Bobby Fischer of the geriatrics?
Bobby Fischer was a renowned chess player; Niles is calling Martin Bobby Fischer because of his inexplicable prowess at the game.