And of course, her primary error is that humans are rational beings. We're not. We're evolved animals, and one of the things we've evolved is the ability to rationalise behaviours that stem from thoroughly irrational sources. That a whole bunch of bright self-made and aspiring individualists who prefer doing to theorising have a lot of time for someone who essentially gave them a way to feel just great about both means and ends which have caused pain to other people+ is hardly surprising; but it's correlation, not cause. Indeed, I suspect that the people who readily accept Rand would basically have thought and acted that way anyway, but would have found an alternative, less satisfying, justification for doing so (for example, the economical justification of the Austrians). The importance of Rand to such people is the moral justification she crafted for them.
+ Note, I'm not passing moral judgement here; what makes us feel guilty about our actions is the combination of empathy with knowledge of the pain we have caused someone else - but we can alleviate that guilt if we can convince ourselves it's for a greater good; and there is no greater good than to have done what is morally right.