Audit The Fed?

I'll admit my eyes gloss over when hearing about some financial issues, the Federal Reserve being one of them. But, I keep hearing people I respect bring it up over and over so I felt I had to watch this short YouTube video (less than 5 minutes)explaining the Fed. Nicely done, by a news commentator.

Still, even after watching the video, I have to ask: What do we do about the Fed? Would things be any different if the money supply were run by congress or a government agency?