I completely disagree. Carrot doesn't think personal is the same as important. He does what he thinks is right, not what he thinks Vimes will like.

That's true. For example, he doesn't understand irony.

In a way, Carrot could be seen as being as cunning as Vetinari - as Vimes (I think it was) observes to himself in one of the books, you'd have to be VERY cunning to appear as simple as Carrot does.

I think it's been made clear here and there in the books (as mentioned in this thread already) that Carrot knows exactly what's up, and uses that knowledge when necessary, but makes it appear that he's just innocent ol' Carrot.

Also, yes, I think respect for Vimes does have something to do with it - not that he fears him at all, but that Vimes has influenced Carrot's understanding of the way the city should work and of the importance of the law as a separate thing from the person behind the law (what better example of that than Vimes, who has his own Watchman?) I think that's one reason Carrot says what he does about not wanting people to follow him just because it's him telling them what to do.

of course he knows but he doesnt want to rule i'm sure it say somewhere in the books he dosent want people doing things because he says so
although i think vetinari and carrot are grooming vimes for vetinari's job
for when he finally retires

Absolutely, Carrot knows although he doesn't openly admit it. Remember Men at arms (that's the one with the Gonne right?). At the end of the book Carrot and Vetinari have a very silent discussion about it. Carrot decides to live his life as a humble member of the Watch!