Much like we never see Niles' wife Maris, we never learn the name of Niles' new dog. He calls her "the new lady in my life," "girl," and "my new best friend," but he never calls her by name.
One of the very few times the hallway between Martin's bedroom and Frasier's bedroom is seen. Also a rare appearance of the inside of Martin's bedroom.
Frasier (Kelsey Grammer) angrily reacting to being defeated by Martin (John Mahoney) is similar to when he loses to Woody on Cheers (1982).
This episode is a typical example of the way chess games are portrayed on TV. In reality, games between advanced players rarely make it as far as checkmate, as the losing player resigns well beforehand, and advanced players would almost never fail to spot an imminent checkmate.