Some people may think that this is just splitting hairs, an irrelevant exercise in taxonomy, to determine who is or is not heterodox. And that would certainly be a complete waste of time and energy. But the problem is that this inconsistency between reasonable policy advice and coherent economic theory is at the heart of the problems with the mainstream, and not just the crazy ones that believe in extreme versions of market efficiency (see for example Lucas’ Milliman Lecture; as I suggested these views could be referred to as the Intelligent Design version of economics. Krugman calls it the Dark Ages of macroeconomics).
As I argued somewhere else (subscription required, or preliminary version free here), there is a symbiotic relation between the best in the mainstream (what David Colander refers to as the cutting edge), that sound reasonable and provide rational policy advise particularly in times of crises, and the hardcore fundamentalists that stick to neoclassical/marginalist principles (despite logical problems). The problem is not a trade off between relevance and coherence in general, as Mark Blaug tried to argue with respect to Sraffians (his point being that Sraffians are rigorous and cannot be relevant for that reason; see the reply by Kurz and Salvadori here). The trade off is a particular problem for the mainstream (that's why Blaug's argument is preposterous).
Rigorous arguments are NOT detrimental for empirical relevance, and they are essential for coherent policy advice. Part of the problem with the current state of the economics profession, what Alessandro Roncaglia has called the cultural roots of the crisis, is that the reasonable so-called New Keynesians, like Larry Summers and Ben Bernanke, were for deregulation and did not see (or didn’t want to see) the crisis coming. There is no intention to revise the foundations of economic analysis.
The whole argument of the best in the mainstream (and even some heterodox economists) is that conventional models are too simplistic and we need more sophisticated models. In this view, the problem is the complexity of the real world. Also, the mainstream is not monolithic, and there are several strands, some better some worse, with a high degree of eclecticism. I find the argument disingenuous, at best. Sure the real world is complex, but the increase in the number of complex models have served since the 1970s as a way of introducing more realistic and often more relevant policy results while maintaining the respectability of the mainstream defense of the sanctity of market efficiency. Some of these models are not even compatible among them, and, it is true that the mainstream is fragmented or eclectic. In this sense, I borrowed the use of the term organized hypocrisy to describe, not the behavior of individual economists per se, but of the profession as a whole.
Organized hypocrisy implies that the mainstream can still maintain that markets are efficient, and that General Equilibrium models are a coherent proof of that (which allows the Tea Party version of the profession to go around and preach Real Business Cycles and Supply Side Trickle Down Voodoo Economics), while at the same time say that there are more sophisticated models, with imperfections, and alternative patterns of behavior, that explain reality. Hence, whether Krugman and other cutting edge authors understand it or not, they have a role within the mainstream which actually serves to perpetuate their hold on the profession. They are there to make the mainstream sound reasonable without the need to rethink the foundations of the subject. Eclecticism is not a good feature of the mainstream, it reflects their lack of coherence and the inability to provide a theory that is both realistic and logically sound.
PS: Eclecticism should not be confused with pluralism. One is the result of incoherence, the other of tolerance with different approaches to economics. For example, institutionalists take a different starting point than Sraffians, but say relevant and coherent things that add to understanding of the real world. A pluralistic approach that encompasses some of the contributions of both schools is, therefore, quite reasonable. The same could be said about other heterodox schools.