The fundamental problem with capitalism is that it is fertile ground for extremist wealth disparity and greed. Our political system should ensure, by law, that excessive greed is punished, wealth disparity is kept in check and taxation is fair. What we would call well regulated capitalism. This was working just fine 70 years ago. Then those who benefited the most from our system realized in the 70s and 80s that they could by influence in congress, hire a bazillion lobbyists, buy commercial time and start 'expert' institutes to flood the zone (media) with FUD.
Unwinding this would probably required another Great Depression and a strong leader like FDR.
Personally, as someone raised by lifelong true-believing far-leftists (and seeing how that didn't really work out, either globally or for those I knew personally), I find myself thinking both left and right are correct in their critique of the other.
The right seem to be correct that you need a market and hence price signals in order to efficiently allocate resources. The problem of running a modern economy is too complex to be handled by a central planner. That's why communism failed. It leads to economic sclerosis, because you can't correctly allocate resources without a market. (There's also a further problem of the concentration of political power, and the heinous concequences that can lead to, but personally I find it hard to work out to what extent that is an intrinsic problem with socialism and to what extent it's simply a consequence of the circumstances that are necessary for socialism to come about - the economic problems seem much more fundamental/intrinsic).
But the left seem to be correct that capitalism is unstable - it leads to increasing economic inequality and class stratification which in turn leads to unequal political power as politics is not distinct from economics, and to a form of economic failure of its own.
That's why The Economist (a pro-capitalist, right-wing journal) had an entire issue a few years ago (around the time of the financial crisis) where they desperately appealed for capitalists to altruistically put the interests of 'the market' and capitalism ahead of their own personal short-term interests.
Since communism collapsed capitalism has shown little sign of being able to 'up its game'. Seems to me that it continues to be as dysfunctional as ever.
People can point to 'social democracy' and some sort of 'middle path', as exemplified by Sweden - but Sweden (and most of Scandinavia) has seen a big growth in the far right, as the Social Democratic parties have been slowly dismantling social democracy and moving to the neo-liberal right, provoking a far-right backlash, just like everywhere else.
The conclusion I find myself left with is that 'nothing works'. Humans don't have any stable and non-destructive means of co-operating in large numbers. Human nature makes that impossible. Ants and bees have maybe hit on a way of doing that, but humans don't seem to be up to the job.
Hence the future is likely to be an escalating cycle of capitalism leading to economic stratification and destroying the conditions necessary for its own existence, followed by social-collapse, war, and either socialism or fascism...which in turn will collapse due to economic failure, to be replaced by capitalism again. And each time round the violence and disorder will get worse.