As for whether the President has any "real power", seriously... whenever he says something wrong, the stock prices drop and the oil prices raise.
And same holds true for the Chairman of the Federal Reserve Bank. Should I be concerned about his lack of foreign policy experience?
As CornField pointed out, the real power in the United States is in the Congress, not the Executive Branch, all the implications of an "Imperial Presidency" notwithstanding. In the end, the President can only do what Congress funds him for. No funding=no action. Period. It is the power of the purse.
The President is the most over-rated position there is. His real power is limited. In every case I can think of since I was born, he is elected based on promises that he has no authority to keep. The President cannot enact universal healthcare or the FairTax or make a cut in spending - all of that is the purview of Congress, as is the funding and declaration of war. He can't even propose the bills for any of these items. More than anything else, he is the saber-rattler in chief.
Yes, you should be concerned about Ben Bernancke's lack of foreign policy experience. I know I am concerned. Alan Greespan's tenure as the Fed Chief showed us exactly how powerful this appointed position really is.
Technically, the President has exactly the same power to propose a bill to Congress as any citizen of voting age. He still has to get a Congressperson to introduce it. The main difference is his access to Congresspersons. The War Powers Emergency Act allows the President to send forth troops in defense of 'national interests', it also allows him to maintain a state of conflict for a certain period of days without a formal approval from Congress.(either 30 or 60 days, its been many years since my last government class)
But at the end of the day it really does come down to 'who has the checkbook'.....