Feyerabend should, undoubtedly, be praised for providing a scathing critique of the status of the scientific enterprise within contemporary society. It wasn't a popular position to take at the time it was written, and it's still not much of a popular position today (except among Creationists, perhaps). It couldn't have been easy to step outside of the imposing influence of the day and say something that nobody wanted to hear. He made people--scientists, philosophers, and laymen alike--critically examine their respective positions towards science and reevaluate their sometimes uncritical conclusions. Yet, in considering this and similar philosophy historically, it's impossible to ignore its blatant irresponsibility, its disastrous effects on thought and objectivity.
Getting down to the main positions Feyerabend takes in this work it's easy to sum them up pretty briefly: There's no set of unwavering and indubitable rules or methods that science actually utilizes in practice; Scientific theories are often incommensurable in that they are composed of fundamentally different concepts that are not reducible to a common measure; Science as a whole has unduly been given a special status in society that it does not deserve, and it's just another ideology and should consequently be separated from the state like religion.
Okay--I'll say at the outset that the incommensurability of scientific theories is a fascinating concept and one that I'm really not informed enough to have any substantive opinion. So I'm not going to comment on it except to say in passing that it seems less of an intractable problem than it's made out to be.
As for method, I think Feyerabend makes gross exaggerations and doesn't sufficiently argue away the difference between contexts of discovery and justification as well as he thinks he does. If we have a theory that is not even theoretically falsifiable because it's claims are compatible with all observable phenomena, it's going to have a difficult time surviving the context of justification. It will eventually wither away in not being able to face empiric criticism. If we have a theory that turns out to be self-contradictory, it will have a difficult time surviving the the context of justification. Yes, it may, for a time, prove its utility in various ways, but it will never be thought of as "right" unless it can reconcile its internal contradictions. Standards are more than arbitrary, historically determined, totalitarian-like, rationalist schemes. Although I obviously can't get into acceptable standards in this space, they do have the function of time and time again successfully removing the crap from science (psychoanalysis, for instance). Feyerabend is right to reject "naive falsification." Of course theories can't explain all the facts in their domain and may be in conflict with some of them. This is fine. But when theories are conflicting with most of the facts in their domains, providing minimal utility, and clashing with very well corroborated theories they are right to be rejected. And it's important to remember that, especially when critiquing Feyerabend, this is a rational rejection.
Now, the separation of science and state. Ridiculous. Absolutely terrible. One of the worst ideas ever put forth. Stop giving tax dollars to scientifically-minded institutions like the National Institute of Health, effectively abolishing it altogether? Or how about having the FDA start endorsing homeopathy, voodoo, and witchcraft for dealing with medicinal concerns? Excellent! Have departments of transportation pay no attention to the physics of bridge building? Yes! Start teaching astrology and magic as viable alternatives alongside astronomy and biology in school? Perfect! Society will be improved immensely! We'll be free of the corrupting influence and ideology of Science! (Feyerabend doesn't explicitly make these claims--except, I think, saying that we should teach "magic" in public schools--but they are natural consequences of his view, nonetheless.)
Feyerabend says, concerning the utility of science, "The questions reach their polemical aim only if one assumes that the results of science which no one will deny have arisen without any help from non-scientific elements, and that they cannot be improved by an admixture of such elements either . . . Science alone [this is sarcasm, here] gives us a useful astronomy, an effective medicine, a trustworthy technology. One must also assume that science owes its success to the correct method and not merely to a lucky accident [italics in original]."
The "non-scientific elements," methods inherent in homeopathy, voodoo, witchcraft, and astrology which lack the rationalism and critical reflection of the sciences are assuredly not going to improve the human condition. They've been tried, and they failed terribly. Certainly science needs to stay creative, but the solution must not be looked for in the practices just mentioned. There's a reason why science is successful. It would be quite a coincidence if, instead of having the "correct method," science hit upon hundreds and hundreds of "lucky accident[s]," over and over again throughout history, continually making life better for people through such "accidents."
Some further comments: Feyerabend is also critical of Lakatos and his "research programmes." I guess originally this work was supposed to be the two each going back and forth, F defending irrationalism in the sciences and L defending rationalism. But then Lakatos died. Shame, because he would have probably thoroughly put Feyerabend in his place. Feyerabend's argument is that, essentially, Lakatos' more liberal versions of some of Popper's ideas are so liberal that, "in so far as the methodology of research programmes is 'rational,' it does not differ from anarchism." Or, to put it another way, that Lakatos is arguing the same thing as Feyerabend himself, but cloaking it in the language of rationalism. Interestingly, Feyerabend says, only a few pages later, that, "Lakatos does not really differ from the traditional epistemologists. . ."
In regards to Feyerabend's own philosophy of science he says, "There is not a single rule that remains valid under all circumstances and not a single agency to which appeal can always be made," and that, "Anything goes." Yet he also says, paradoxically, that the "essence of empiricism" and the "important part of all theories of confirmation and corroboration" is "counterinduction [italics added]." He goes on to conclude that, "Counterinduction is therefore, always reasonable and it always has a chance of success [italics added]." In other words, scientists would be stupid not to use counterinduction with the introduction of every new theory. Counterinduction sounds strangely like "a rule that remains valid under all circumstances," no?