The book that Martin (John Mahoney) is reading to Daphne (Jane Leeves) whilst she is sick is none other than "The Rose and the Rapier", first mentioned by its author (Dierdre Savage) in the Season Three episode The Adventures of Bad Boy and Dirty Girl (1995).
Frasier and Niles see a production of The Man Who Came to Dinner and describe the plot to their father, Martin, played by John Mahoney. A year after this episode aired, Mahoney starred in a production of the play at Steppenwolf.
When Frasier is convincing a trepidatious Niles to go to the cabin with Laura and Beth, he says, "Don't you think it's time you grabbed for the brass ring?" The expression "grabbing for the brass ring" originated in the late 19th and early 20th century when carousel riders on horses would grab for a brass ring from a mechanical arm as they went by.
Megan Mullally guest stars as an interior designer; in the hit series Will & Grace (1998) she plays an interior designer's assistant.
The title is from "Two for the Seesaw", a play written by William Gibson. The original Broadway production opened at the Booth Theater in New York on January 16, 1958, ran for 750 performances and was nominated for the 1958 Tony Award for the Best Play.