There's a very random reddit thread right now that talks about the way Martin Sheen puts on a jacket in The West Wing. The unusual way in which Martin Sheen does this is, according to the top comment on the thread, due to a physical condition he has which left one of his arms substantially shorter than the other (Erb's Palsy). Just a bit of trivia to keep in the back pocket for...whenever you want to talk about Martin Sheen.
Also, if you think this is more of a West Wing thing, here's Sheen doing the same jacket flip in Badlands.