Here's the short: Salmon, in the New York Times Book Review, wrote that he thinks Wolf's new book, The Shifts and the Shocks, is too dense for a general audience. Wolf wrote a response letter accusing Salmon of being unqualified to review the book (because he isn't an economist).
There's been a continued back and forth in the few days since.
Salmon's point, as he made in his original review and in a follow up letter to the editor of the Times, is that Wolf's book is hard to read. "Some books are a pleasure to read; others are convoluted, technical and abstruse. A reviewer should indicate which books are which," he writes.
Wolf, on the other hand, says that the arguments in his book require precision - a precision that you can't get using the linguistic shortcuts that Salmon suggests in his original review. Salmon writes that he should have used the term wages instead of "real unit labor costs." Wolf explains:
...an index of wages differs from one for "real unit labor costs" in two ways: It is a nominal index, while the latter adjusts for changes in the price level; and it ignores relative change in the productivity of workers (so important for understanding shifts in competitiveness), which the latter includes. One cannot understand what I am arguing if one thinks these terms are equivalents.
The larger question here seems to be whether Wolf is writing for economists, in which case precision is of the utmost importance, or for a general audience, in which case clarity is important.
"My point was basically not that he was wrong. I know he is absolutely right," Salmon told Business Insider. However, he said, Wolf's prose is a slog, and "It's worth saying that for anyone who might be tempted to buy this book."
That said, Paul Krugman is also out with a review of the book, with quite a different verdict: "Since the new sort-of consensus [on the economy] is clearly much more realistic than the pre-crisis complacency, Wolf, the chief economics commentator of the Financial Times, has performed a very useful service by putting it all together in one readable book."