I disagree on Util classes. They're fine so long as they're as well-tested as regular code and divided up by the libraries they depend on. (Put all your IO utils in one place, all your database utils in another, and so on.) Guava has lots of nice utility methods for Maps, Lists, streams, and so on.
I don't necessarily see a problem with Util classes, either. He didn't really say why they're bad. Actually, I guess he didn't describe why we should do most of the things he recommended, but I agree with most of the other advice.
