There really no free market.Profitable trade is monopolized

Any of the big problems we face. I am always surprised that people think and expect that a market can/should solve problems, while its only purpose is selling and buying. You could as well ask what problems get solved by handclapping.

The 'free market' is not designed to solve problems, it is designed to maximize profits - it's the same reason 'good businessman' is not a qualification for elected office - a government exists to serve and protect its citizens, a business exists to maximize profit. Two completely different and often conflicting purposes

Also we do not have free markets, they are carefully manipulated to protect the wealthy, no one who believes in free markets should be uttering things like 'too big to fail'

1 is pollution and other forms of general destruction of the environment. #2 is our health. If corruption of the government counts then that's up there too.

What free market?

the student loan debt crisis (at least in the U.S., don't know if it is a problem in other nations)

Income inequality. For those who say increasing the min wage will be offset by inflation, min wage would be $20/hr today had wages kept up with productivity. Has to work both ways.