Before the final credits there is a dedication to Robert Crosby, a deceased sound technician who worked on 23 episodes of "Frasier". He had also worked on 118 episodes of Cheers (1982).
This episode is the first to discuss the political views of some of the main characters. Marty is revealed to be a conservative, while Frasier and Niles are more liberal. In real life, Kelsey Grammer later publicly embraced more conservative views, including support for Donald Trump.
Martin's mention of Lyndon Johnson lifting up his shirt to show his scar refers to an famous moment in LBJ's presidency when he did just that--in front of reporters and photographers--after he had had gall bladder surgery.
During their conversation about Phil Patterson's (Boyd Gaines) belief that he had been "beamed up" to an alien vessel, Niles (David Hyde Pierce) says to Frasier (Kelsey Grammer), "Are you kidding me? I'm a doctor, not a miracle worker!" This is likely a reference to the famous catchphrase "I'm a doctor, not a...(insert various professions)" spoken by Dr. Leonard McCoy (DeForest Kelley) in Star Trek (1966).
The celebrity caller in this episode is Sydney Pollack who, as Holden Thorpe, is an obnoxious right-wing Congressional candidate who insults Frasier (Kelsey Grammer) over the air, driving Frasier to film an endorsement for his opponent.