When Tommy and Harry are playing charades, Harry mimes something, and Tommy guesses McHale's Navy (1997), in which French Stewart appeared earlier that year.
When Sally asks Dick (in an English accent) if the trial's over, Dick responds, "Eliza?" This refers to My Fair Lady (1964), in which Cockney flower girl Eliza Doolittle is turned into a cultured member of high society.
When Dick gets his jury duty letter, he says, "Winter, spring, summer, or fall, all you have to do is call, and I'll be there." These are lyrics from "You've Got a Friend" by Carole King.
Dick's tirade in jury deliberations is not only a parody of a famous line from A Few Good Men (1992), but an obvious impression of Jack Nicholson's speaking style, as he says, "You want the truth? Well, I can't handle the truth!"