I agree that Bernanke shouldn't be reappointed, and I would go further than this by not replacing him with anyone. In fact, I'd abolish the Fed and institute free banking (real free banking, not the phony kind the U.S. had during part of the antebellum era).
I think the Fed is no more competent to use interest rates (or anything else) to control inflation or maintain full employment, than Soviet Gosplanners were to put the market clearing number of refrigerators or other consumer goods on the store shelves in the USSR, and goods of the same (and ever improving) quality, and at the same costs! The problem is much the same in both cases--the impossibility of planners having all the disparate bits of knowledge available to buyers and sellers in a market economy, and then using these bits of knowledge to replicate "the results of human action but not of human design," as Hayek put it. George Selgin dscusses the Fed's problems in chap. 7, "The Dilemma of Central Banking," of his book The Theory of Free Banking.
The Fed can't prevent bubbles; indeed, it is their primary cause. The Fed can't reliably pop them either, for the same reason that Soviet planners can't reliably know how many refrigerators to produce. Asking the Fed to do these is like putting the proverbial fox on guard of the chicken coop. Free banking solves the problem for the most part. Selgin, Schuler, Dowd, White and other historians of free (and central) banking have written extensively about free banking's superior historical record in terms of economic stability, booms, busts, and financial panics.
Comrade Bernanke and his crew are unbelievably arrogant in thinking they can solve these sorts of problems, which should be left to the free market.