In the course of a review of Scott Ryan's book on Rand, Greg Nyquist makes an interesting suggestion that Rand's view of "the problems of universals" may have originated with Richard Weaver. I quote in part:
Rand's decision to regard the problem of universals as central to philosophy and Western Civilizations remains, even at this late date, twenty years after her death, a bit of mystery. Given that she had no clear understanding of its historical background, it is odd that she should have considered it the main source of modernity's problems. Where did she ever come up with such a notion?
My guess is that she got it, second or third hand, from Richard Weaver, the great conservative philosopher and literary critic. In 1948, Weaver published what is still probably the most important contribution to conservative philosophy in America, a slender volume entitled Ideas Have Consequences. In the book, Weaver argues that the "dissolution of the West" is the consequence of "the fateful doctrine of nominalism." "Like MacBeth, Western man made an evil decision, which has become the efficient and final cause of other evil decisions," wrote Weaver. "It occurred in the late fourteenth century, and what the witches said to the protagonist of this drama was that man could realize himself more fully if he would only abandon his belief in the existence of transcendentals. The powers of darkness were working subtly, as always, and they couched this proposition in the seemingly innocent form of an attack upon universals. The defeat of logical realism in the great medieval debate was the crucial event in the history of Western culture; from this flowed those acts which issue now in modern decadence." [2-3]
Weaver regarded William of Occam as the prime culprit in the nefarious attack on universals. "It was William of Occam who propounded the fateful doctrine of nominalism, which denies that universals have a real existence. . . . The practical result of nominalist philosophy is to banish the reality which is perceived by the intellect and to posit as reality that which is perceived by the senses. With this change in the affirmation of what is real, the whole orientation of culture takes a turn, and we are on the road to modern empiricism." 
In the late forties and early fifties, Rand still traveled in conservative circles. She probably heard about Weaver's book from her conservative acquaintances; and although she would have violently disagreed with Weaver's platonist interpretation of the issue, the suggestion that the crisis of the West stemmed from the old scholastic controversy between those who regarded universals as "real" and those who did not appears to have borne fruit in Rand's own philosophy.