Rose. Oh, she is the most perfect, most beautiful creature in all the universes.
Well, no, scratch that. She is nowhere close. Of course, no one person, let alone a human, could even be perfect, in any way. So obviously Rose is imperfect. She has her flaws, just like everyone else.
Rose got into fights. Not real, huge fights, mind you, but verbal fights, with the Doctor in particular (this may have been because they were stuck with each other, but that's beside the point). The Doctor hates their fights, because often they're about something silly and end up with her storming to her bedroom and the Doctor left to tinker with the TARDIS to distract himself. Rose gets over herself in a few hours, and usually they make up by watching a film together on the couch. Only once had a fight lasted for days. The Doctor felt worse than normal, because this time it wasn't so silly, and it was all his fault. Rose had been giving him the silent treatment, and he had no idea why. So he asked what was wrong, and with enough coaxing she finally gave in. She spoke softly at first, and her voice sounded scared; it was enough to almost make the Doctor apologize for anything he had ever done wrong, ever. She had whispered so quietly that the Doctor didn't quite understand what she was saying at first, but figured it out soon enough ("You left me for dead."). He had tried to give her a hug by way of apologizing, since that usually worked, but she pushed him away and raised her voice just a bit ("How did you expect me to get back home? Mickey and I couldn't fly the TARDIS, so what were we supposed to do? You have no idea!"). The Doctor even tried admitting he was wrong, which did no good. Then Rose's face would turn pink (such a lovely shade, too) and she was near shouting ("You're a Time Lord, you'd think you'd be a bit smarter and consider what you were leaving behind before you ran off with a beautiful French aristocrat! I mean, I suppose you had reasons- not very good ones- but you didn't have to leave us for dead!"). And the Doctor stayed silent, fearing he would say something wrong. Then her voice got quiet again ("I just- I dunno, I just thought I meant something to you.") The Doctor had looked at her face, examined it, seeing how so very hurt she was, and he hated it. A face that beautiful was changed by eyes beginning to puff up, and turn red. Then, the worst part came- or the best part, if you saw Rose the way he did in that moment. She stood up and took a deep breath, and the Doctor dared not say anything. Rose raised her hand up and brought it down almost too quickly to see, brought it down straight onto the Doctor's cheek- and hard, too. Harder than he had ever been slapped by Jackie. Then Rose marched off to her bedroom, and the Doctor watched her go, and how much he wanted to go running after her and scoop her up and tell her that he was so sorry, and that she did mean something to him, she meant so much, and she was so beautiful and so worth everything, could not have been measured in human terms. So he didn't go after her, and he stayed put in the console room, where he really ought to spend more time anyway. In fact, he's in there now, thinking about how glad he is that he and Rose haven't fought in ages. This so-called flaw isn't disappearing, of course, but that doesn't matter, because a flaw is just an attribute, really.
She isn't even the most beautiful woman. Not to say she isn't beautiful, because she is. And she is the most beautiful woman he has ever seen. But are certainly more beautiful beings out there (none of them mattered so much, of course). No, Rose doesn't have perfect skin, or the "ideal" shape, or anything of the sort. But she is beautiful to him, not only because of her absolutely stunning face that the Doctor "accidentally" finds himself staring at sometimes, but also because of her gorgeous personality. Not that that doesn't have flaws of its own. Of course, Rose can be selfish, and jealous, and tons of other things that also describe many other people that the Doctor has met. To anyone else, Rose would probably just be an ordinary girl occasionally seen walking about ("Well, thanks a lot," Rose would say sarcastically when the Doctor told her so).
So why does he care for her so much? He's cared for his companions for centuries- but not like this. This is different. But why? The Doctor thinks it best not to even try to name all of the reasons. Unless they could all be piled into one big reason- he loves her simply because she is Rose Tyler, and she is so beautifully imperfect.