I've collected criticisms of Austrian economics for many years in my index Austrian Economics. But a sheaf of miscellaneous criticisms may not be as clear as a parable.
The owner of a ship noticed that his ship was filling with water. Being an educated man (if not nautically trained) he knew there were many possible causes for water in a ship: leaks in the hull, the bilge pump being broken, waves washing over, condensation, and even the crew urinating in the hold. He heard the bilge pump running, he saw water from waves pouring in the open hatches, but worst of all he smelled urine in the hold! Being sensible, he ordered the crew to shut the hatches and then gave them a lengthy, stern harangue on hygienic use of the head. While he was lecturing the crew, his ship sank due to a combination of causes: large, unobserved leaks in the hull, a bilge pump that was running but not pumping correctly, and condensation that had shorted out warning circuitry.
Now, it's easy to write a story to justify or ridicule any course of action, any philosophy. Indeed, that described Ayn Rand's fiction. But my purpose here is to illustrate ways in which the owner failed to think correctly. Ways which are STRONGLY analogous to Austrian economic methodology.
In every theory-rich subject, there can be a multitude of explanations of cause. For example, there might be 5 possible causes for a specific problem, be it inflation or disease or whatever. All or none of those causes might be valid. If all of them are valid, some might be unimportant because they cause very little of the problem or cause the problem very infrequently or cause the problem only under specific circumstances. But more than one of the causes might be quite important, singly or in combination. Economics is just such a theory-rich subject.
There is no way to identify from philosophy which of these might be the case. You need to be able to observe enough to quantify these factors. However, Austrianism is staunchly against measurement: indeed, it is innumerate because it does not use measurement. Rothbard, Mises, and Hayek railed about how measurements were philosophically invalid.
In the parable, the owner did not investigate condensation; he presumed the pump was working correctly without measurement; he did not attempt to measure leaks; he presumed (again without measurement) that the water sloshing in the hatches was the right amount to explain the filling; and he distracted the crew from finding the real problems with his own assumptions and moral haranguing.
Since Austrians are innumerate, instead they must rely on their assumptions, which needless to say tend to have a very right wing bias. Science does not work that way. Nor can Austrians really defend their assumptions: no assumption about the real world is totally true which means that there is fallacy in all their logic about the real world. They make up for this in bluster and old-fashioned appeal to their own authority.
When confronted with real-world problems that could have multiple causes, logical verbal models are insufficient. You MUST introduce measurement and mathematics into your models if you want to have any hope of valid answers. Logical verbal models are sufficient to specify possible chains (or networks) of causation, but telling which are significant is a quantitative problem that requires measurement.
This is not a new position: it is basic to science and ought to be basic to philosophy. Hume said it very clearly 260 years ago:
Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.
David Hume, Enquiry Concerning Human Understanding, 12, "Of the Academical or Sceptical Philosophy"