As we are nearing the end of the official time for discussing G!G!, I thought there were a couple of points to throw out (having re-read what is really quite a fascinating discussion).
It seems to me that in some respects, Vimes and Vetinari are (in spite of the apparent difference in the characters at the beginning) really very much alike. Vimes, when we first meet him is lying in the gutter in front of the Watch house talking to himself about his love of the city. And it is the city (not the much later in the series mentioned woman) that he is in love with. Straightening out his ramblings, what he says is
The city is a woman who has strung you along and let you fall in love with her, then kicked you in the teeth! She's a bitch! And just as you begin to hate her and get her out of your heart/mind, she opens her great rotten heart to you. And you never know where you are with her. Only thing you were sure of, you couldn't let her go. Because she was yours, all you had.
Vimes and Vetinari both live for the city, and at this point are only dimly aware of each other. Vimes has seen (we know from later books) the horrors of prior Patricians, and I think we can fairly infer that he dreamed of making a difference, of making Anh-Morpork a great, wonderful city. But meanwhile, Vetinari has also decided to make AM a great wonderful city and his method of doing that has all but destroyed Vimes's occupation.
But neither man can function to save the city without the other. Vetinari seems to have been totally oblivious to Wonse's jealous plans to overthrow him. And that is one of Vetinari's failings. He has chosen to make himself so disconnected from humanity, for which he has little use, that in order to make the city work, he leaves himself open to someone like Wonse. And while it is true that Vetinari could have gotten out of the dungeon, he doesn't leave his safe post until the last minute.
Thus, in a peculiar way, it is the Watch (assisted by Lady Sybil and Errol) who save the city. In their own inept way, they attempt to protect and serve. And had Wonse survived, Ank-Morpork could not have continued to exist.
Vimes embraces humanity--he sees within himself the darkness that he sees in society, and that he keeps under control partially by drunkenness. But he also sees the things that are wrong in the city, but is powerless to do anything about them, and so he drinks to ease his pain--the pain of being all too human.
Vetinari doesn't want to be king any more than Vimes does--or even than Carrot does. And that peculiar moment where Vimes thinks about the trousers of time is the point when Vetinari (who recognizes the sword, and the implications of it) gives it back to Carrot without any formal recognition.
Vimes's preferred weapon (that he uses to save Lady Sybil) is not the sword of a king, but the cleaver. He doesn't like horses or all the trappings of (or most of the) nobility. But at the end Vimes recognizes the similarity between his view of the city and his view of Sybil who in some senses represents the city. Vetinari keeps the trappings of royalty (as have prior Patricians) but he acts using the power of his status as a member of the nobility to institute the kinds of reforms that have made the city a safer, more prosperous place. He makes the city run--but he does not want to be King.
At the end of the book, Pratchett neatly ties things off. And, as Tony mentioned-- perhaps he leaves things open. I think he knew he was going on with the series, but perhaps not. "Perhaps the magic would last. Perhaps it wouldn't. But then what does?"