The piano piece that "Elegant Iggy" plays at the dinner party is "Fantaisie Impromptu" in C# minor, Op. 66, by Frédéric Chopin.
Jim and a lady at the party sing part of "Two Sleepy People", a song written by Hoagy Carmichael with lyrics by Frank Loesser. This was cut from the DVD release, probably due to copyright restrictions.
This Episode was The Final Taxi To Air on ABC