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In the original "Bicentennial Man" story by Isaac Asimov, the robot manufacturer was named "U.S. Robots and Mechanical Men" (as in Asimov's other robot stories dating back to 1942). Around 1971, a new modem-manufacturing company took the name "U.S. Robotics", partly to honor Asimov. Unfortunately, since in the movie the robot manufacturing company is not portrayed positively, the real-world company asked the filmmakers to use a different name. Hence, "NorthAm Robotics". There are a few places in the film where you can see the old name and logo.
All of Andrew's jokes as he regales the family were unscripted. Robin Williams ad-libbed all of the jokes, and the other actors' reactions to them are completely real.
Adam Bryant, who appears as the android head, has been Robin Williams' stand-in for more than a dozen films.
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 female robot, Galatea, is named after the statue brought to life by the gods in the Pygmalion myth.