I think he's deeply misunderstanding economics. First we do have at least two paradigms that are universally accepted:
(1.) the gains from trade/the law of supply and demand (the "theory" is supply and demand but of course the accepted understanding of the gains from trade is what motivates the behavior in question). The law of supply and demand is like natural selection for economics. It supports everything and is universally accepted.
I think the paradigm shifts we go through are also fairly thorough and happen at about the rate that they do in any other science. In my mind the first real thorough paradigm we had was Ricardianism. Then there was marginalism (a micro paradigm), then Keynesianism (a macro paradigm). And I'm not sure we've ever come out of the Keynesian paradigm.
Moreover, Keynesianism as a paradigm is relatively uncontested. This is what Arnold Kling refers to as the AS/AD mentality. I think Kling unfairly caricatures the perspective, but that's another discussion entirely. We don't use the word "Keynesian" to refer to the whole paradigm, of course. When we use it in every day language we're really refering to a more specific class of models and perhaps even some policy persuasions. So we oppose "Keynesian" to "Monetarist" and "New Classical", etc. when really monetarists and new classical economics are very firmly in the Keynesian paradigm - they just tweak a few assumptions in their models to try to solve puzzles that they feel earlier work didn't solve. The paradigm, though, is fairly stable. To borrow Gary's words from the comment, the big debates you see between economists "regard specific mechanisms". I'd probably agree with Gary that a lot of models are comparable to UFT work - but then nobody ever claimed that we've broken a new paradigm in economics and nobody in physics is quite ready to claim that for UFTs yet. So? This is where the paradigm leads us. Do seemingly intractable puzzles bother Gary? Kuhn says these are solved in a couple ways: first, with new empirical technology, or with a paradigm shift (and often the former facilitates the latter). We're getting new empirical technology all the time. We have longitudinal employer-employee household datasets now. We didn't have that in the 1990s. Now we can test the new advanced in theory in the 1980s that was just awarded a Nobel Prize last year. Who knows where these advances are going to eventually lead us? I don't.
But Gary's simply wrong on the paradigms. We have a few big ones and we definitely have laws that are universally accepted.
People get really weird when they talk about the scientific status of economics, despite it's very long and very firm status as such. The reason, it seems to me, is that people don't like to be pinned down and studied. That's what we do to inanimate objects and that's what we do to animals but we like to think there's something "special" about humans. We don't like to be reminded that we're just a highly evolved primate and that we are as amenable to scientific study as other primates.