We get this question often enough that I thought a general announcement that I could refer back to in the future might be in order. What's said here is my take and shouldn't be taken to speak for Wes, Seth, or Dylan.
I recognize the cultural influence of Ayn Rand and that it would be a public service to have an episode at some point explaining, at least, why most academic philosophers think she's so bad. I think this has likely been done already, and much more thoroughly than we would do, by others (I'm not even going to hazard to link to anything right now, as the whole point in not doing the topic is not wanting to take the time to adequately research it; just do a fricking Google search yourself). My sense is that her readings of other philosophers is so superficial, and her arguments are so overly simplistic, that the proper antidote to her influence is just getting a philosophical education. In other words, you can take (if you like) every episode we've recorded as a response to Ayn Rand, and if you can really hold on to her doctrines (e.g. that Kant and all epistemology after him is just a matter of denying "simple and self-evident axioms") after immersing yourself in these difficult debates then, well... I will be very surprised.
I read both her Introduction to Objectivist Epistemology and The Virtue of Selfishness in college and did give them some serious thought at the time. I would personally be open to doing an episode where we cover these works, but I think only after we've already covered the main ideas in their more sophisticated forms given by other philosophers. We've already done some of this work, and some more of it is planned. Here's a non-exhaustive list (and perhaps those more in the know about this than I am can correct any mischaracterizations that may creep in to my account):
1. Rand is both a psychological and ethical egoist: people always do what they perceive to be in their interest, and they should do this. Her innovation is in the latter portion of this, but if the psychological egoism part is untenable, then there's little hope for ethical egoism. Psychological egoism was very much a live issue with Hobbes and those reacting against him. In our Hobbes episode, we brought this up briefly but didn't give it a serious shake. By the time of Hume's ethics, the issue was more or less dead; Pat Churchland also went into the science of it with us. Perhaps most seriously, these types of egoism assume a pre-made self, whereas on episodes like those on Hegel and Sartre, we've argued that there's no such thing.
2. The main gist of her epistemology is that unless we can clearly define a word, we don't know what it means. This comes out of Aristotle (not a part of him that we've read so far), but in our recent Wittgenstein episodes, we've gone in depth into what's wrong with it: words arise out of concrete situations of use. To come up with a definition in the sense of a set of necessary and sufficient conditions is to rip the word out of its actual uses and more or less stipulate conditions for its application across the board. In some cases (e.g. with mathematical terms) this is justified, and in some cases (e.g. with "good") it does violence to our complex intuitions on the matter. Positing a definition for "good" or "truth" or any of your other heavy duty philosophical terms is a matter of asserting a positive philosophical theory, not just of getting clear about these words that we all already understand.
3. Rand claims that much of her philosophy comes from Reason itself. We've done some work, as in our Schopenhauer episode on the principle of sufficient reason, to explain why this is nonsense. Reason in the sense of logical truths just gets you from premises to conclusions; it doesn't provide the premises, and the number of "self-evident propositions" is minuscule. The philosophy of logic is an area that we surely owe some episodes to (not soon, though), but you can listen to our many epistemology episodes for more discussion of what self-evidence might consist of.
4. Her main appeal is in her anti-conformity, as in The Fountainhead where the architect protagonist rejects the shallow and nonsensical expectations of his peers, teachers, customers, etc. I think there's an interesting conversation to be had here, and I'm not sure that we've had it yet. MacIntyre and Aristotle argue pretty convincingly that the kind of radical independence from your fellows that Rand recommends is impossible and/or pathological, but there's a also a strain of existentialism from Nietzsche's "Übermensch" to Kierkegaard on "the crowd" to Heidegger on "Das Man" ("the one") that recommends a similar rejection, so some more detailed discussion of this topic from us at some point would be nice.
5. Of course it's her libertarianism that's most at stake in today's debates. We are planning an episode on Robert Nozick, who better presents the philosophical foundations of this view. Our Locke episode does take a crack at analyzing one attempt to derive property rights from self-evident principles ("the law of nature").
After we've completed #5 along with the rest of our current batch of long-planned political episodes (Rawls, Marx, Adam Smith), then I'll bring up with the guys the idea of treating Rand much like we handled the New Atheists; there's plenty that's interesting about the fact that Rand has had such an influence for us to talk about, even if we feel like we can deal with many of her arguments by summarizing the discussions of earlier episodes as I've done above.
It's definitely hard to motivate ourselves to spend time on works we know to be bad when there are so many great works out there. One idea we thought up is having a pledge drive such that we'll cover her if we receive some amount in donations dedicated specifically to that end. However, I'm not sure why fans of Rand would be particularly eager to pay us to deliver what they will doubtlessly take to be an unfair portrayal of their idol. I can say that given the approach of the show, it would likely not be appropriate for us to get a Rand defender on with us for a debate. Again, I'm sure you can get enough unhelpful back-and-forth of that sort elsewhere on the web.