For anyone who hasn't heard of this book yet, the basic premise is that for the entire history of capitalism, capitalist economies have returned a higher rate on investments ("capital") than the corresponding rate of GDP growth, and that this imbalance necessarily leads to an ever-increasing concentration of wealth for the investor class.
Capitalism isn't really all that old, as economic systems go, but he's using the broadest possible data sets available to compare the rate of return on capital (typically ~5%) to GDP growth (typically ~3%). With very few short term exceptions, the standard progress of capitalism is for people who have wealth to build more wealth, relative to the rest of their societies. Capitalism contains no mechanism by which this concentration of wealth can be avoided.
The parts of this book that have taken the most heat from critics are primarily centered around his proposed remedies. The historic remedies have been catastrophic economic collapses, like wars that bomb capital investments into rubble, or revolutions that appropriate private property for the state. Both of which are really bad for GDP but even worse for capital return, resetting the balance. If you make everyone equivalently poor, the process can start all over again.
Some people seem to oppose the book on purely ideological grounds, because it smacks of Marxism. Marx thought that the capitalist west contained the seeds of its own destruction, and in broad strokes this book is making the same case. Logically, though, saying you disagree with an idea because it reminds you of another idea you disagree with doesn't really count as a refutation of either idea.
I'd be interesting to hear more opinions from this crowd. I think this book spells out some ideas that have been widely discussed here before, and then projects out into the future the foreseeable consequences of the game we're all playing. Those early MMM threads with titles like "what if everyone retired early?" were dealing with some of the same ideas.