First, ideological self-identification is a very poor tool for describing voter beliefs. Elites understand the bucket of issue positions that fall into categories like "liberal" and "conservative," but research shows that most people don't. And the relative numbers of self-identified liberals and conservatives often bounces up and down in ways that don't seem to reflect actual changes in the public opinion landscape.
I don't think he actually emphasizes this enough. It's pretty obvious that outside the folks who pay a lot of attention to these issues, people don't know much about what these labels mean. For example, "Libertarians" were more popular among Democrats than Republicans, in a recent Pew Research survey. Now, is that because Democrats like the small government, free market ideology of libertarianism and Republicans aren't so hot about it? Or is that "libertarian" sounds a bit like "liberal"? I'm gonna go with the latter.
This also glosses over the fact that even among politicians, the meanings can be pretty fungible. Certainly in the international sense, David Cameron may be closer to an American "liberal" than an American "conservative," even though he's the leader of the Conservative Party! But even here at home, there are many flavors of liberal and many flavors of conservative. Ideological labels are like music genres, good for vast generalizations but flawed when examined closely.
His other points are excellent, however. The piece is well worth reading.