The first time I watched Vertigo, I found it slow, and a little dull (as most do at first, or maybe always). I gave it another shot after it was announced at the top of Sight and Sound's film poll, and was glad I did. I rewatched at least part of it again a few years later, enjoyed it more still. This time, having rewatched it this month, I was convinced it was Hitchcock's best film, and one of the richest tragedies I've ever seen.
I don't think any other of Hitch's films has the psychological understatement or richness of Vertigo (which isn't saying too much, admittedly). However, watching this time, and asking myself to sympathize with these otherwise unsympathetic characters, it was painful, honestly. They are such damaged human beings, and yet so fully human.
With all that in his mind, he has no alternative but to seek psychiatric help, and when he sees a woman he thinks looks like Madeleine (not knowing it's the same person), he feels the need to "rescue" her again; bring her back to life, if you may. She lost her, but Judy symbolizes the possibility of bringing her back.
I especially appreciate Thief12's comments, although I take issue with the one quoted. I don't necessarily know if it's rescuing her that's what he desires. Interestingly, I read that the director James Gray saw a class element in trying to restore the middle-class Judy to the upper-class Madeline, which I can totally buy.
However, in my own experience, I see the most realistic explanation for Scottie's attitude to be the intense, reactive, and obsessive desire to express power and control over something that has been taken or that you no longer have any control over. In all honesty, there's no reason that the clothes, makeup, and hair would have been a significant aesthetic reason for Scottie's attraction to Madeline (he surely could have fallen in love with Judy). Nor does he at any point try to change Judy's behavior. He simply wishes to exhibit complete control over her outward appearance. In many ways, it's like the definition of rape, although I would not go so far as to say that Scottie does this, but that rape is about power, not sex, Scottie's attempts to control Judy are about power, not sex. He does sincerely love Madeline, but the emotional trauma of losing her, of having failed to control her, manifests itself by his trying to have complete control over Judy. When he finally does, it's a sort of solution to the problem. No longer needing to demonstrate to himself his control over the situation, he can begin a domestic relationship with her (which we see, however briefly).
Of course, alternate arguments are always encouraged, but that's my reading of the film, which is why it's so painful. This is the second time Judy has been willing to forfeit all autonomy for a man, but unlike the first time, now it's about love. It's about the fact that when Scottie had power over her when he believed her to be unconscious after her attempted suicide, he did not claim it. He respectfully undressed her and put her into bed. Judy was awake for that, no doubt. How gentle and caring Scottie must have been for Judy to have allowed that to happen.
Vertigo stands at the closest point to which love and fetishism intersect. Each moment of love can be seen as having shadings of sexual obsession and compulsion; each moment of sexual obsession and compulsion have shadings of love.