Adam Bryant, who appears as the android head, has been Robin Williams' stand-in for more than a dozen films.
When Andrew regales the family with jokes, the jokes themselves were unscripted. Robin Williams ad-libbed all of the jokes. The other actors' reactions to the jokes and their laughter are real.
The aria that Andrew is listening to when he first uses the record player is from Dvorak's opera "Rusalka." The opera is concerned with the fairy-tale story of a water nymph who wants to become mortal for love.
The three rules that govern Andrew's behavior are the Three Laws of Robotics, originally defined by Isaac Asimov in his science fiction stories.