I don't think anyone is surprised at the reaction to Mankiw's forthcoming JEP article. Discussions about the distribution of income get people excited. I read Mankiw's piece, and thought it was a decent summary of what economists have to say about the distribution of income and wealth. Mankiw's own views certainly enter into it, but he makes it clear when he's relying on serious research, and when his argument is based only on casual empiricism.
There are two main points. First, Mankiw argues that the increase in dispersion in the income distribution in the United States is due mainly to two factors: technological change driving an increase in the relative demand for highly-skilled labor, and a scarcity of high-skilled laborers. He could add international trade as a third factor - the idea that wages of low-skilled are lower than they would otherwise be because of lower barriers to trade and a plentiful supply of low-skilled labor abroad. But the point is that most of the change in dispersion is due to factors that have little to do with government activity (except perhaps trade policy), i.e. with tax policy and regulation. I think those conclusions are not particularly controversial among economists who have worked in this area.
Second, Mankiw argues that, to the extent that there is something "wrong" with the income distribution, there are better ways to do the fixing than by changing the way we tax income. If government regulations serve to protect inefficient monopolies, or allow financial institutions to practice what is essentially theft, then we should change those regulations. If patents promote inefficiency, we should change our patent laws. If opportunities are poor for people living in inner cities, we need to be thinking about how we can promote education in those neighborhoods.
Tax policy is something we have to be careful about. Micro evidence seems to tell us that the incentive effects of income taxation are small. But, for example, work by Manuelli, Seshadri, and Shin tells us that, if we look at the full array of tax and retirement policies, and take account of lifetime decisions about capital accumulation in general equilibrium, then the incentive effects are big-time.
So, for the most part, I agree with Mankiw. I think we also a agree about "enrichment" programs for kids. This actually goes much beyond summer camps. At Washington University in St. Louis, where I work, undergraduate tuition fees for the 2013-14 academic year will be $44,100. What do students (or their parents) get for their money? As Mankiw says, a lot of it looks like consumption rather than investment. Indeed, a walk through campus can remind you of a summer camp. Rich parents certainly want to send their kids here, but there's no guarantee that sending them here will perpetuate family wealth. Apparently, taking economics helps, though.