Arthur refers to a "television fellow who claims he's just 39." This is a reference to Jack Benny, a radio, film, and then-television star who used to have a running gag where he would lie about his age, claiming to be 39 when he was in fact much older.
Though the character, Arthur, is celebrating his 65th birthday in this episode, the actor, Charles Ruggles, was actually 74 years old at the time.
Jim turns off the rock-n-roll tune Arthur and Betty are dancing to and puts on "The Blue Danube" in its place. This waltz was written in 1866 by the Austrian composer Johann Strauss. "The Blue Danube" is the name this waltz commonly goes by in English. It's full title in German is "An der schönen, blauen Donau" which is literally translated as "On the Beautiful Blue Danube."