Babbitt was partially based on real-life savant Kim Peek, who passed away in 2009. Barry Morrow became fascinated by Peek upon meeting him, which is why he decided to make a movie about him. (Source)

When Dustin Hoffman met Kim Peek, they reportedly rubbed noses upon parting, and Hoffman said, "I may be the star, but you are the heavens." It's unclear whether the story is true, though. (Source)

Hoffman's portrayal was also based on a man named Peter Guthrie, who (unlike Peek) was actually on the autism spectrum. (Source)

When Rain Man was shown on plane flights, they dropped the scene in the airport where Raymond lists all the planes that crashed. It's a big omission because it basically explains why they have to drive to LA instead of flying, but airlines, uh, don't like talking about plane crashes when everyone is mid-air (who knew?). The only airline which showed the scene intact? Qantas, which, according to Raymond, "never crashed." (Source)