Francis Ford Coppola gave Robin Williams camping gear to spend the night in his backyard and ten dollars to spend at Toys R Us before shooting the film.
If you look closely at the costume of the woman dressed as a wine bottle in the opening scenes, you'll notice the wine she's dressed as comes from Francis Ford Coppola's vineyards.
Tom Hanks was the original choice for the lead role because of his performance in Big (1988).
Jack's condition (of aging four times faster than usual) is a somewhat exaggerated but nevertheless real illness, known as Werner Syndrome.