1) His concept of capital is ambiguous, though to be fair, one could argue that it is the thing and not the language that is ambiguous. However, in most of the passages I have read so far (2/3 finished) he treats capital as a social relation -- that is, income claims based on supposed property rights -- rather than, as neoclassical economists do, as a resource comprising produced means of production. This is closer to Marx than to neoclassical economics. None the less, I would say that Marx' concept of capital is both richer and less ambiguous.
2) He doesn't explain his predictions of the growth of inequality, but having done some work of this kind (and heard or read a great deal more) I think I understand it. Not sure, understand, but he refers to "simulations." A standard method in 21st century macroeconomics is to write a "mathematical model" of a process by which an economic formation at one period is transformed to produce the different economic formation at the next period. The mathematics will include some random variables -- in Piketty's case the age at which proprietors die and leave bequests would be randomly distributed across the population, for example. These mathematical and random variables are then coded as a computer program and run, with a whole series of transformations, and trends and averages recorded from the computer program. We then try to tinker the math up so that, when we start with the numbers for, say, 1990, the results look a lot like the real world for 1990-2007. (Nobody tries to predict crises.) Then predictions are made from the tinkered-up computer program. This sort of works, sometimes.
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