Question: What is the academic standard for "scholarly" and do Ayn Rand's writings meet this standard? If they do, what standards are those who claim Ayn Rand's philosophical writings are not scholarly using?
Answer: It is my view that scholarly writing has several distinctive characteristics: It shows careful reading of primary sources and a thorough knowledge of the debate on an issue. It takes care to address traditional questions in the literature. It is written in a dispassionate tone and follows the forms of citation such as you find in The Chicago Manual of Style.
Now Ayn Rand's philosophic writing generally is not scholarly in this sense. She does not demonstrate a detailed familiarity with primary sources or with the academic debates of her time. (But she does incisively grasp the essentials of the issues at stake in any topic she addresses.) She brushes aside many traditional problems of philosophy without a detailed treatment, and when she does treat a classic question (the problem of universals, for example, in Introduction to Objectivist Epistemology), she does not devote much attention to proving how her ideas fit into the tradition. (But, her analysis of classic problems often cuts through to an innovative solution, and she lays out the case for her own view clearly.) Rand is a passionate writer and wrote most of her non-fiction as cultural criticism, addressing how her views applied to the real world. She was always rather cursory in her citations. (But she always took care to explain the reasons for her views. And it is to her credit that, unlike many scholars of philosophy in today's universities, she was committed to the idea that philosophy must apply to real life in useful ways.)
Rand was not, in my view, a scholar of philosophy. She was a philosopher. A thinker can be both, but need not be. In fact, few of the great works of philosophy are scholarly in the full, modern, academic sense. Wittgenstein does not offer scholarly philosophy in his Philosophical Investigations. Plato does not write in scholarly fashion. Marcus Aurelius does not write in scholarly fashion. Nietzsche does not write in scholarly fashion. Nor does Rand. A scholar shows he knows a literature. A philosopher shows he understands the fundamental issues in life.