Riviera is notable for his exclamation upon entering a room of "Hi, everybody!" which is followed by a response of "Hi, Dr. Nick!" from the other characters.
He has operated on the Simpson family a couple of times, notably when Homer could not afford a heart bypass from his regular doctor. Lisa attended the live audience(!) for the operation and saved the day by guiding the obviously clueless Dr. Riviera through the operation.
He is also shown as an inventor/huckster (in the style of Ron Popeil) on "I can't believe they invented it".