He argues that the worries about the coming death of the Social Security trust fund are greatly exaggerated. He argues that the virtues of privatization are oversold because stock market returns down the road are unlikely to stay at 7% in real terms. Finally, he argues that the system is not really in crisis. There’s no reason to privatize.
I think he’s maybe 2/3 right. The troubles with the trust fund are essentially mythic and the current pay-as-you-go structure of the system (which he likens in a bizarre analogy to the highway tax) can surely be sustained if the body politic so desires.
I also think he’s right about the overhyped virtues of privatization though I think he’s only half-right. It’s not just that stocks may be headed for lower rates of return in the future. The real exaggeration of the privatizers is that the current system has a sizeable redistributional component that reduces the implicit return under the current system for citizens with above-average earnings histories. My suspicion is that any successful privatization plan will have to retain this component in some form. One way is to have the government match private contributions for the lowest-income individuals.
But my biggest disagreement is Krugman’s elevation of the status-quo into something virtuous. His last section is called "Privatization is a solution in search of a problem." He’s right that we can save social security down the road by devoting an increasing share of the budget toward it. Sure, it’s fixable. But why would we want to fix it?
Just because social security can be made solvent or the government can keep some version of this so-called social contract between the generations, why we would want to do that? Imagine starting from scratch and creating a mammoth program with a hidden distributional element that’s so complex that no one can know what it will be worth in the future other than relying on a meaningless annual letter from the government that purports to tell you what you’d get from the system if you retired today?
And while Krugman is right that some critics of the system say misleading things about the trust fund, the proponents of the system have been saying misleading things about the trust fund since about 1934. Until recently, most Americans actually thought that their payroll taxes went into "their" account or something like it or at least into the pockets of the elderly. It’s only recently that some folks have caught onto the fact that much of it goes to fund general government expenses.
If the current system is such a good deal, why isn’t it voluntary? When I propose that solution to defenders of the status quo, they always smile and say, oh that wouldn’t work. And why not? Because, they explain patiently, people would opt out—what makes the system work is that we’re all in it together. I await a better answer. I don’t think there is one.
Finally, it must be said that all of the privatization plans on the table aren’t really about privatization. They’re about mandatory savings along with allowing the coerced savers to invest in private sector assets. I suspect that’s a step in the right direction, but my preference would be for the government to get out of the retirement business and let us as responsible and compassionate adults take care of ourselves and those who are too poor to save much for their old age. End it, don’t mend it. 
The right reason to favor some flavor of privatization has nothing to do with trust funds and nothing to do with rates of return. It has to do with treating citizens as adults, responsible for ourselves (and others if we choose) rather than the current system which treats us as children.