In the pre-credits teaser, Harry is struck multiple times in the head, ultimately speaking with a southern accent, saying: "Now the liberals want you to believe that more government is going to solve your problems." This impression is likely intended to evoke H Ross Perot, who ran a third party presidential campaign during the time this episode was filmed.
This isn't the first time John Lithgow has appeared in drag. In The World According to Garp (1982)), Lithgow played Roberta Muldoon. He also appeared in drag at the conclusion of Raising Cain (1992) as one of Lithgow's character's multiple personalities.
The title of this episode - "I Enjoy Being a Dick" - is a reference to the song "I Enjoy Being a Girl", from the 1958 Rodgers & Hammerstein musical, "Flower Drum Song".