Even a perfectly rational, error-free free market can fuck up, in the sense that it doesn't lead to the most optimal outcome of all possible outcomes.

Markets are dumb incremental optimizers. They often fall into social traps that are locally stable.  They are good at fine tuning once the starting conditions have been set, but they are totally blind to finding the "correct" starting conditions in the first place.  They don't see the bigger picture because they are incapable of cognition and design.

The situation for real markets is not as simple as that because the space of "all possible outcomes" is not static and  is itself dependent on previous outcomes. But there are a lot of cases in practice in which the above still temporarily applies.

To me, market intervention is justified if the existence of a social trap is easy to prove and there is a strong consensus among participants that everyone would be better off if the trap could be escaped.  

To me, things like air traffic control and other public goods are a no-brainer.  Monetary policy, not so much.  Sure, unemployment can be alleviated, but the problem is that nobody really understands the long term and unseen effects of interest rate and money supply manipulation. We are messing with a chaotic system. It might become even more unstable as a result of our intervention.  Also, there is a lack of consensus about an "optimal" rate of unemployment and so on.

I don't know whether democratic government is the best Leviathan. DACs seem like a promising and less error-prone alternative.  Anyhow, a good government should not be a decision maker but merely an executioner of consensus.  Thus it is incapable of making strategic errors in the first place.