I think a big problem with most press secretaries is they don't have any real world experience. They go to college and go straight into being a politician's aide, and then move up the ladder from there.
All press secretaries ought to have to work for a while at a weekly newspaper, or somewhere that will, as Grivusangel noted, expose them to different kinds of people. They need to learn to work and earn a living on a shoestring so they will understand what it's like to live frugally and deal with people very different from themselves. This is crucial when having to explain difficult policy in terms that won't cause revolution.