Maybe this is just a coincidence and this has to do with another team, but in the 1984 movie "The Karate Kid", in the scene where Larry Drake and his buddy are drinking beer and putting the bottles on Miyagi's truck by the beach, Larry Drake is wearing a red baseball cap with a curly "W" logo. The logo looks exactly like the current Nats curly "W". Maybe it was a cap representing the old Senators or the Nats but the movie didn't have anything to do with Washington. Maybe there's another team out West with the same colors and logo.
Anyway, I thought it was funny to see. The scene is at about the 1:20 mark of the movie if you happen to have a copy of the DVD on hand. Check it out.