["Ayn Rand," by Talbot, taken from Wikipedia.Com; this image is used in accordance with fair use.]
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Ayn Rand had a few different sins, depending on the level of analysis.
She was a brilliant novelist and philosopher. Her "Introduction to Objectivist Epistemology" was arguably her greatest purely philosophical project. In my opinion, it is about on the level of Descartes' Meditations. Her work is somewhat similar to Hannah Arendt's, but it is more overtly classically liberal and pro-capitalist, and she doesn't have the same Heideggerian influences. She is reviled by academics and social conservatives. Some of their critiques of her are valid, although, for the most part, their critiques merely reveal their respective biases.
As far as her genuine shortcomings are concerned (in my opinion): there are two major ones that are related to her work, and two others that have more to do with her personal life.
In her work, her biggest shortcoming is that she doesn't acknowledge the debt she owes to other philosophers; especially Friedrich Nietzsche and Rene Descartes. Her metaphysics and epistemology owe a massive debt to Descartes, and her ethics owes a massive debt to Nietzsche. She does not acknowledge this, and tears down their respective bodies of work in her writings in a way that does not do them justice. This, I think, is reflective of the fact that she tends to adopt an extremely dismissive attitude towards most other major philosophers (which accounts for the valid aspects of academics' hatred of her). The second problem with her work is her failure to fully flesh out her answer to the free will problem, and the mind-body problem. Beyond those two issues, her philosophy is well thought out and consistent, albeit devoid of proper acknowledgment of her reliance on the contributions of past thinkers.
As for her personal life, she tended to alienate rather than build bridges, and her very public love life attracted a lot of criticism (perhaps some warranted, and perhaps some not) from social conservatives.