Ron Paul is a hack.
Now that we have that out of the way, let me share what I have gathered on this topic, but I wouldn’t call myself an expert.
The Federal Reserve is currently required to produce annual reports that include an independent audit of of its financial statements. Furthermore, the Government Accountability Office conducts periodic reviews of the Fed.
As I understand it, the key area of disagreement is that the Fed is extremely reluctant to share detailed lending records that would show which banks were seeking help from the Fed. Proponents of the “audit the Fed” bill argue that the public has a right to know where any “bailouts” are going. The flip side of the argument is that the Fed makes aggregate numbers available (e.g., how much was loaned out in total) but that releasing specific information on specific banks would needlessly undermine investor confidence in those banks, as well as discourage banks from seeking assistance when they might need it the most. I believe the “audit the Fed” bill is specifically designed to require detailed disclosure of these activities to the Government Accountability Office.
There is also a debate on the degree to which Fed deliberations on monetary policy should be subject to disclosure. Right now, the discussions are largely kept out of public release for fear that the decisions on monetary policy would become politicized.