All of the title cards are references to Tennessee Williams and his plays ("Tennessee, Anyone," "Cat Fight on a Hot Tin Roof," "Suddenly This Summer," "The Night of the I Wanna" and "The Bath Menagerie.")
"Conk" does indeed mean "nose" in British slang. As a verb, it can also mean to be hit on the nose or head.
The paper Frasier is trying to read at the breakfast table is The Seattle Times from 16 March, 1997. The episode was broadcast on 6 May that year.
Dan Butler (Bob "Bulldog" Brisco) and Marsha Mason (Sherry Dempsey) also worked together on the film, I Love Trouble (1994).