The Space Shuttle seen in this film is the Columbia in its STS-1 configuration --- the only one with a white external fuel tank. The spacecraft had arrived at Kennedy Space Center in March of 1979 and was scheduled to launch late in that year, but was delayed until April, 1981 due to engine and thermal protection system problems. Hence, the production was forced to use shots of the Shuttle on the launch pad, but an Apollo-era Saturn V rocket for the lift-off shots.
Pictures press release announced that actress Judy Graubart ("Lisa") would make her theatrical film debut in Simon (1980).
The "Institute for Advanced Concepts" was filmed at the then-new Bronx Development Center, a residential care facility for physically and mentally handicapped children. It was completed in 1977 and could accommodate 380 children and was run by the State of New York. However, it was allowed to decay and the state closed and sold it to a private developer who partially remodeled the modernistic building seen in this film and renamed the site the Hutchinson Metro Center in 2003.
California governor Jerry Brown appears on the cover of the mock-up New York Times cover used in the film.