Mitch's three children are named Arlene, Bennett, and Dorothy. These are the names of the celebrity panelists from What's My Line? (1950): Arlene Francis, Bennett Cerf, and Dorothy Kilgallen.
Jim (Christopher Lloyd) goes on a long rant about Star Trek (1966). Three years later, Lloyd would appear as the main villain of Star Trek III: The Search for Spock (1984).
During his diatribe about the cancellation of Star Trek (1966), his favorite show, Jim's one criticism of it is that the leader of the Romulans was given lines no Romulan would ever say. This is a bit of an in-joke for Trek fans. Mark Lenard, who played the militaristic Romulan Commander in the classic Balance of Terror (1966), returned the following season as Spock's father, Sarek, a member of the philosophically opposite but (at the time) biologically identical Vulcans - a role he reprised across different spinoffs. Hence the same actor playing two different characters from two different species who look, but don't think, alike. Lenard also portrayed a Klingon in Star Trek: The Motion Picture (1979), becoming the first actor to play all three of the franchise's main alien species. All of which undoubtedly helped to fuel Jim's confusion.
Thirty-one-year-old Martin Short (and his character's hairstyle/fashion sense) bears a resemblance to Brandon Tartikoff, who at age 32 was the youngest president of NBC's entertainment division at the time this episode aired.