No, not monitor & regulate...the standard is a little bit more like "protect the public from fraud and unfair practices."
Greenspan's roll was as a market cheerleader -- for almost 20 years he did everything in his power to keep it from crashing...choices that were ultimately very poor for the market and the economy in the long run...as he himself has now admitted.
The very big piece that you are missing is that "everyone" loved Greenspan when he was in office and he largely did whatever it took to keep that love flowing. What you should take from the Frontline special is that no one -- not the liberals, the conservatives, the experts or the public -- wants to hear the bad stuff (or the ugly truth) when the good times are rolling. Everybody works to promote the good times because that's what the public wants to hear. It is only when the good times end that the public wants to take names and knock heads. It's too late at that point to make any difference at all.
Because the United States has a free market economy, theoretically, the highs and lows in the market should be affected only by supply and demand. According to the free market theory, any institution with enough clout to sway the movement of the market — like the government — should stay out of the way and let nature take its course. While the U.S. government doesn’t directly intervene in the stock market (say, by inflating the prices of stocks when they fall too low), it does have power to peripherally affect financial markets. Since the economy is a set of interrelated parts, governmental action can effect a change.
Government has obligation to make sure its citizens are not cheated (robbed). So they monitor most financial securities (including stock) and setup organizations like SEC to regulate transaction of these securities.
No direct regulation (they will bit interfear with free-market) or price manupluation. But rather indirect regulations, making sure that companies don't cheat. But some like madoff can still do it, escape below the lense of regulators.
Greenspan was part of team (FED directors), who took some decision on monitory policies (interest rate) which effect some dynamic of financial market in future, and it cannot be proved that if he did otherwise what would have be the current state of financial market.