1. Problems with "paradigms": The concept of a "paradigm" is far too vague. If one tries to specify paradigms more precisely, one discovers they are not so much like Kuhn describes them. They are far more varied, complex, and certainly may behave differently than the way Kuhn claims.
Net assessment: What Kuhn describes is not exactly on target, and it is more than likely that "paradigms" -assuming there are such- are vastly more complex than he describes them, and so do not necessarily condition the historical patterns in science the way he suggests. Nevertheless, it is rather widely conceded that there is something like a "paradigm" in the sense of a conceptual framework, or a language, which stipulates standards by which acceptable and unacceptable science is judged which is operative in much of mature science, though not necessarily all. Certainly today one commonly assumes this as an operating hypothesis on which to do philosophical, historical, and sociological research in the sciences, in particular if that historical or sociological research is going to be made to grind some philosophical axe. (The publication of such scholarship has experienced extraordinary growth.) In any event, unless current writers are specifically referring to Kuhn's own model, the word "paradigm" has today lost much of its popularity and many contemporary philosophers of science, though indebted deeply to Kuhn, want to distance themselves from his perspective and so tend to avoid the word.
2. Problems with "revolutions": Closer historical analysis reveals that "big" paradigms tend to reduce to overlapping smaller paradigms and periods of normalcy seem less like long tranquil periods and resolve into myriads of smaller revolutions separated by relatively short periods. Normalcy doesn't seem so normal, and revolutions, at every level, seem much more normal.
Net assessment: Kuhn was locked into the concept of "revolution" from the nature of his task (to write a book on scientific revolutions). Something like paradigms probably do function in science and there are levels at which science operates normally and levels at which it does not. There are no doubt some changes of paradigm which are "revolutionary" but there may also be "evolutionary" changes which are less wholesale than Kuhn's "revolutions" demand, and this sort of change may be more typical of the growth of science. One might speak of the dynamics of paradigm change and look for the "rationality" which governs such "evolution" of the conceptual schemes or frameworks within which science operates, and thus recover from "irrationalism" suggested by Kuhn's more radical concept of "revolutionary paradigm shifts." Furthermore, such dynamics need not display the artificial pattern of revolution- normalcy - crisis -revolution that Kuhn imposes.
3. Problems with "rationality": Kuhn's position on theory choice is unacceptable because it rests on much too radical claims about lack of ability to "translate" from one paradigm to another. Radical meaning variance is simply not historically the case and examples intended to display it are exceptional and contrived. Since in most of the modern world, what is called "science" is so called because it serves as the very model of what it is rational to believe about the natural world, -to the extent that we assume if it is rational to believe anything, it is rational to believe science- if Kuhn's philosophy of science denies the rationality of science, so much the worse for his philosophy of science.
Net assessment: The "rationality crisis" is premature. Kuhn himself has "retreated" to a much less radical position than his first edition suggested. Most philosophers today are anxious to find that there are, after all, some standards which determine rational acceptance or rejection of beliefs about the world, although they are almost surely not what one thought they were on the traditional empiricist/positivist analysis. In fact determining just what they are will require great historical and sociological research and one should not expect answers to be easy or simple. Furthermore, it is improbable that there is one such set of standards for all science. Instead of seeing science as the progressive building of theories on the observed facts and/or refuting them by the observed facts, the growth of science now would have to be characterized in terms of the selection of one dominant theory, by the community of practitioners of that science, from perhaps a large number of competing rivals. Such a selection is made by appeal to a large number of factors which will vary from science to science and from one period in that science's history to another. Of these many factors, appeal to the observed facts (which are partially determined by the theory or paradigm) is only one, and often not a deciding one.
4. Problems with the "sociology thesis" on theory choice: Kuhn's theory entails an idealist metaphysics in which thought determines reality. Insofar as science is committed to the description of a single observer independent reality (an objective description) Kuhn's description of science misses the essential nature of science, for idealism is incompatible with the prima facie realism of science. For Kuhn doing mature science requires operating in a particular world-view accepted for sociological-historical reasons. As such Kuhn makes science a kind of ideology, differing from rival ideologies only in the degree to which it is endorsed by "The Establishment" (whatever that might be).
Net Assessment: Kuhn did not intend to go that far! This much, at least, is clear from his explicit statements, but where he means to stop remains hard to justify. One might, of course embrace the extreme relativism of this interpretation of Kuhn's claims; indeed, at least one philosopher has done so: Feyerabend. But the majority of philosophers would hold that though Kuhn may have hit upon much of importance that was ignored by the positivists, if his analysis leads this far, it is, ipso facto unacceptable.