Chris Giles of the Financial Times has been diving into the source data that underlies Thomas Piketty's Capital in the 21st Century, and he says he's found some problems. The details are here. Piketty's response is here.
Is Giles right? Experts will have to weigh in on this. But Giles' objections are mostly to the data regarding increases in wealth inequality over the past few decades, and the funny thing is that even Piketty never claims that this has changed dramatically. The end result of Giles' re-analysis of Piketty's data is on the right, with Piketty in blue and Giles in red. As you can see, Piketty estimates a very small increase since 1970.
Now, if Giles is right, and there's been no increase at all, that's important. But it's still a surprisingly small correction. The fundamental problem here is that the difficulties of measuring wealth are profound enough that it's always going to be possible to deploy different statistical treatments to come to slightly different conclusions. There's just too much noise in the data.
In any case, I'm not taking any sides on this. The data analysis is too arcane for a layman to assess. But it's worth keeping an eye on.