You may find it interesting that [Murray] Rothbard actually disagreed with Mises on the falsifiability and empiricism of the action axiom. I'm surprised to see no-one has mentioned this in the thread...Turning from the deduction process to the axioms themselves, what is their epistemological status? Here the problems are obscured by a difference of opinion within the praxeological camp, particularly on the nature of the fundamental axiom of action. Ludwig von Mises, as an adherent of Kantian epistemology, asserted that the concept of action is a priori to all experience, because it is, like the law of cause and effect, part of "the essential and necessary character of the logical structure of the human mind." Without delving too deeply into the murky waters of epistemology, I would deny, as an Aristotelian and neo-Thomist, any such alleged "laws of logical structure" that the human mind necessarily imposes on the chaotic structure of reality. Instead, I would call all such laws "laws of reality," which the mind apprehends from investigating and collating the facts of the real world. My view is that the fundamental axiom and subsidiary axioms are derived from the experience of reality and are therefore in the broadest sense empirical. I would agree with the Aristotelian realist view that its doctrine is radically empirical, far more so than the post-Humean empiricism which is dominant in modern philosophy.[snip]If, in the broad sense, the axioms of praxeology are radically empirical, they are far from the post-Humean empiricism that pervades the modern methodology of social science. In addition to the foregoing considerations, (1) they are so broadly based in common human experience that once enunciated they become self-evident and hence do not meet the fashionable criterion of "falsifiability"; (2) they rest, particularly the action axiom, on universal inner experience, as well as on external experience, that is, the evidence is reflective rather than purely physical; and (3) they are therefore a priori to the complex historical events to which modern empiricism confines the concept of "experience."You can find the whole article here if you want to read it.
[*] I believe that he has read Man, Economy and State cover-to-cover, which is more Rothbard than I'm likely to get through in my entire lifetime.