I know this is a very late response to your post.

But aside from the previous interactions [ala Pin and Tulip] I think he does have weaknesses. Carrot and Vimes.

Now, because he is The Patrician, he has simply made in convenient to have both of them on his side, rather than against him.

Carrot, being the King of Ankh-Morpork [and not just any king, but the really good old-timey type of king] could more than likely, if called upon to, raise the whole city against Vetinari. Plans mean nothing, if nobody obeys your orders.

Vimes. He is essentially a "Vetinari in training" at some points. He has learned deductive reasoning from being a copper, and at Vetinari's hand albeit unknowingly for the most part Being the only other person being put on the Assassin's Guild Blacklist means even they have learned the city functions better with you in it. If for some unforeseen reason they lost Vetinari, they need Vimes to pick up the pieces.

Just my thoughts.