I'm skeptical of the whole experience angle. The president has a legion of people assisting him, and many of them are experienced. He also has access to experts on any given topic, whether because they're attracted to government service or because he can throw huge sums of money at them.
I see a very specific area of core expertise.
(1) You can't look like a doofus. Well, you have to at least get people to vote for you. You can't forget Poland.
(2) You have to be able to make connections with people very fast. (Duh?)
(3) You have to be able to understand when people are putting you on, understand when people are using you, and understand when people are lying to you.
(4) You have to know who to listen to when you don't have specific knowledge about that area.
I think it's very telling that one of the most well-remembered American presidents was also an actor. I don't think doing a good job with the presidency is as much about getting an "A" in political science or law school, or being the type to do it, as much as it is about understanding people and the systems they create.
EDIT: Or in other words, you need leadership skills. Past that specific law, strategy, technology, or regional information may be a bonus, but I don't think that any one area is as critical as knowing who to delegate it to who can make the right decisions. The President will always have more than he can handle or ever hope to give the attention it deserves.
