Hmm? What negative character traits?
To me, Vetinari is the ultimate pragmatist. It's not for nothing that some people have compared him to Lorenzo de' Medici (also known as "The Magnificent" - for various reasons, which I won't go into here. The wiki-article has enough to explain why.)
Personally, I think Louis XI of France, or Henry VII of England, also qualify (though they had to govern an entire country, not just a city-state). Anyway.
Suffice it to say - and this is only for readers who don't know him very well - Vetinari is a subtle character; "The Spider King", to borrow the epithet applied to Louis XI.
The only plausible "negative character trait" I can think of is his hatred of mimes, which isn't that negative to me. He has a good working relationship with the major players like Vimes and Carrot, as well as the leaders of the major guilds. He works hard and expects other people to do likewise. He uses language with care, and never says something unless he means it. Surely none of those are a negative. *shrug*
His devotion to Wuffles is touching, and makes him more human. But it says something about him that, under his administration, Ankh-Morpork
functions as a city for the first time in a century. Politically, it is stable, which allows it to make money (and become powerful) like never before.
Naturally, making money isn't the whole point of a city. But at least A-M isn't subject to a revolving-door patricianship (like what happened under Lord Winder, Lord Snapcase, etc.)
One last point: of course Vetinari is a tyrant. But I'd argue that his enlightened tyranny is - paradoxically - far more transparent than many modern democracies I'd care to mention. I'd rather put Lord Vetinari in charge of Australia than any of the Prime Ministers we've had since John Howard's retirement in 2007, and that's saying something.
Vetinari's enlightened despotism reminds me of Sir Humphrey's point to Hacker, when the minister receives information about underhand dealings between British arms suppliers, middlemen, and Italian red terrorists. He wishes to raise the issue with the PM, and mentions this to Sir Humphrey. Humphrey advises him against opening ‘a can of worms’:
Humphrey: Government isn’t about morality.
Hacker: Oh, I see! what is it about, then?
Humphrey: Stability! Keeping things going. Preventing anarchy. Stopping society falling to bits. Still being here tomorrow.
Hacker: But what for? What is the ultimate purpose of government, if it isn’t for doing good?
Humphrey: Minister, government isn’t about good and evil, it is only about order or chaos.
Hacker: And it is order for Italian terrorists to get British bombs? And you don’t care?
Humphrey: [disdainfully] It is not my job to care. That’s what politicians are for. My job is to carry out government policy.
Hacker: Even if you think it is wrong?
Humphrey: Well, almost all government policy is wrong... but frightfully well carried out.
Hacker: Humphrey, have you ever known a civil servant to resign on a matter of principle?
Humphrey: [surprised] I should think not! What an appalling suggestion!
Hacker: For the first time I fully understand that you are only committed to means, and not to ends.
Humphrey: Well, as far as I am concerned, minister, and all my colleagues, there is no difference between means and ends.
Hacker: If you believe that Humphrey, you will go to hell.
Humphrey: [smiling] Minister, I had no idea that you had a theological bent.
Hacker: You are a moral vacuum, Humphrey.
Humphrey: If you say so, minister.
I suppose it's just as well that Vetinari uses his formidable intelligence to keep A-M together (i.e. keep the A-M guilds from going to war with each other). If Vetinari followed the advice of someone like Lord Rust (in Jingo), the temporarily united A-M would declare war on "Johnny Foreigner" and ... who knows. Even if A-M won, it would find more problems than opportunities, more frontiers to defend and angry people to pacify than it was worth bothering with (as Tacticus points out in his book).
But that's just my take on Vetinari. No doubt other people have their own opinions.
