Yes, the fear of flying is a popular one. One that I also think was influence by Dean. I remember him saying he hated flying, everyone thinking that was a good chuckle since he played Superman.
Though it may have been actor-influenced, I think this characteristic is really valid. Perhaps, because it's been so well justified in fanfic. It makes sense that someone who's used to flying under his own power would feel highly uncomfortable in an airplane that he doesn't control and is trapped in.
Sara