Popper claimed that falsifiability was the foundation for the scientificity of any theory: if it cannot be falsified, it is thrown out; if it can be tested (and therefore potentially falsified), it is thrown out if such falsification succeeds. his particular criticism of Marxism was that this falsifiability was not present in the theoretical framework that Marxism comprised.
Poppers own Rationality Principle was no better, apparently, and he gave up the 'falsifiability' criterion for this model:
"The adoption of the rationality principle . . . does not play the role of an empirical explanatory theory, of a testable hypothesis. For in this field, the empirical explanatory theories or hypotheses are our various models, our various situational analyses. It is these which may be empirically more or less adequate; which may be discussed and criticized, and whose adequacy may sometimes even be tested. And it is our analysis of a concrete empirical situation which may fail some empirical test, thereby enabling us to learn from our mistakes." -Popper/VerikukusIt is worth noting at this point that the much-revered Ludwig Von Mises had a lot in common with Popper. Mises' 'Praxeology' follows much the same model as Popper's RP (purposeful action and all that), and the contempt for inductive reasoning, reverence for the deductive, is shared. It shouldn't come as a surprise, therefore, that they were close colleagues, often corresponding and supporting each others' theories. Historicism is another target of Poppers, and Mises agrees there, as well:
"No general rules about the effects of various modes of action and of definite social institutions can be derived from historical experience. In this sense the famous dictum is true that the study of history can teach only one thing: viz., that nothing can be learned from history. "It is not my point to "defame" either thinker (I've read them both and I think they each have their own valuable insights). What is concerning, however, is the fundamentalist doctrine - that inductive logic has no place in certain fields. While reading any of their deductive arguments, its hard to ignore the issue of probability that still invades them. Furthermore, the double standard in attacks on Marxism - hardly contained to Popper's criticism, mind you - are merely artifacts of a century and a half of Western works pervaded with anti-Marxist doctrine - perhaps for the simple reason that the state and corporate structures relevant in academia have an overarching interest against communist economic theory.
-Mises, "Theory and History"
More on Popper's Rationality Principle:
"What Popper says regarding the status of the R.P. is not very clear; actually, at times, it is confusing. For example, at one point, he claims that the R.P. is a) “an almost empty principle” and that it should not be regarded as an empirical or psychological assertion that a wo/man acts always rationally. And, then, he adds that b) the R.P. is both “clearly false,” and that, though false, it is “a good approximation to the truth” ( b) contradicts a) for if it is false it cannot be empty; it has a content that is false). In other words, Popper’s scheme of social science involves a law, the R.P, which is both nontestable, therefore not amenable to falsifiability, and false (it has been falsified); yet, he claims that this is the way to go about it." -Verikukis
Popper's doctrine ultimately resolves itself into a distinct set of facts (that is those studies deemed falsifiable and deductive without having been disproved - verifiable in distinct settings) and grants greater weight to them; theories which don't fit this mold are abandoned. In terms of giving weight to these particular "trusted" theories, he is worth consideration. However, narrowing one's approach to such facts requires that one abandon a number of avenues of inquiry - such as many of the tendencies of psychology, sociology, economics, and even Quantum physics (some of Einstein's theories of which are notably non-falsifiable).
In fact, falsifiability presents its own dilemma, namely in that the focus of science must be shifted away from the above fields and towards those fields which have prevalent and prolific study - "facts on the ground." However, it is a logical consequence of this approach that the focus is shifted toward the interests of a particular demographic - that which has the means, avenue and interest to study the given issue. Those which expansive wealth, of course, are disproportionately represented in this demographic.