Kirk did not know who Khan was, or what he was capable of.
I'm not sure I'd buy that. Kirk visibly had his suspicions about the identity of his new passenger, and OTOH he knew
very well who Khan Noonian Singh, Prince of Millions, was.
Kirk's inquiries seemed to merely confirm what he already suspected. And significantly, his treatment of Khan did not change all that much with the confirmation: Khan had been under watch at sickbay originally, and was now placed under watch in his cabin, after spending a brief time dining with the Captain.
Which is consistent and believable if Kirk was such as fan of Khan as he claimed in the briefing room scene. He'd recognize what Khan was capable of, but he'd not see the superman as an immediate or direct threat, not when Kirk had the upper hand in intelligence (that is, Kirk knew who Khan was while Khan didn't really know who Kirk was).
Kirk misjudged - not Khan's character or abilities as such, but his persistence, his will to conquer and control, and the fact that Khan would choose to apply those attributes of his to Kirk's starship.
Timo Saloniemi