A few economic historians have tried to show that he was wrong about one thing or another. His analysis of the Speenhamland law (wage subsidy) is probably fatally flawed (see, for example, the eh.net encyclopedia entry on the poor law), which is why I didn't discuss it here, although it comprises quite a bit of the book. I don't think it compromises his larger points, however.

Some have also tried to show that Polanyi was mistaken about the ancient economies, that they were really market economies, but I think that line of argument is much weaker. Not that markets didn't exist, but (although I'm not an expert on this) they probably were not nearly as important as they are now, which is all Polanyi was really trying to say.