Kirk definitely did not have an affair with Rand or with any woman under his command. Kirk's womanizing is greatly exaggerated. If you look at the actual record, you see various common themes:
Women who attempt to seduce Kirk, often employing mood-altering methods to induce romantic interest, but still failing to overcome his professionalism (Eve McHuron, Helen Noel, Nona, Elaan).
Women whom Kirk coldly seduces/manipulates as a tactic in the course of doing his job (Lenore Karidian, Andrea, Sylvia, Shahna).
Women Kirk has genuine, deep feelings for but either lost or had to leave in the pursuit of his duty (Ruth, Areel Shaw, Edith Keeler, Miramanee).
This changed somewhat in later seasons, as Kirk was pushed more into the mode of the conventional '60s action hero and given more and shallower entanglements (his liaison with Drusilla the slave girl being the most egregious and out-of-character example). But for the most part, his relationships with women were not what you would see in a womanizer.
There is no way in hell that he had an affair with Rand. He wouldn't even look at her legs until she pathetically begged him to. She practically threw herself at him and got nowhere. His dark, uninhibited half in "The Enemy Within" found her desirable and assaulted her, but the intact James Kirk was a professional, a military man, and he never would've allowed himself to get sexually involved with someone under his direct command.
And Todd is right -- Kirk did not "nail" Helen Noel. They flirted a bit at the party, but nothing else happened, and Kirk was embarrassed to be reminded of the flirtation afterward. It was Helen who implanted the fantasy that they had had a romantic encounter -- which, if you ask me, was a gross breach of her professional ethics, imposing her own sexual fantasies on a patient who was under her care and in a highly suggestible state. It was then Dr. Adams who implanted the idea that Kirk loved Helen -- but in spite of that suggestion, Kirk was rather easily able to overcome his desire for her, resume his professional attitude, and rather coldly send her into a highly dangerous maintenance shaft. If Kirk could so easily shunt aside a conditioned feeling of deep, devoted love in favor of being a hardass commander, then it should be obvious that he would never let his libido overcome his professionalism toward his female crewmates under any circumstances.
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Besides, we all know he was secretly in love with Spock. 
