If Count Dooku has one major flaw, it's... well, the obvious answer if you were a Jedi would be that it's a pretty massive flaw that he runs around killing people, but he's quite sure he's justified in that. But that one flaw of Dooku's, that he might even be willing to admit, if you put it the right way...
Well, it comes from how Dooku's spent his life being the smartest person around.
He was smarter than his family. He was smarter than his friends, to whatever extent he had any. He was smarter than his teachers. He was smarter than the Jedi Master who is typically considered to be literally the wisest being in existence, and it wasn't even close. Even the Sith he's met, who at least were capable of holding up the other half of a conversation with him some of the time, were never really all the way at his level.
And of course that isn't a bad thing. Being more intelligent would of course be correlated with getting more things correct, with achieving more success; what else would it even mean. But he's missing something that most people have learned, that they've incorporated into their basic intuitions. When other people are wrong all the time, when he can see the gaping holes in any argument they even try to mention, Dooku's never had any point where he's had to notice to himself that actually no, he was wrong, they were right.
And so he doesn't even check.
Most people have experience arguing, with others and with themselves, thinking about each of the many possible answers and figuring out which, if any, is right. And if Dooku had ever met someone more intelligent than himself, had ever realized that oh, they were right, he might have been able to do that to himself, might have been able to realize to himself that just because the most obvious argument supported something didn't mean he couldn't actually have been wrong. He might have been able to ask himself the obvious questions that he would ask of other people's points, seen the obvious flaws in himself. But that's not a reflex he's ever really been trained into.
Intelligence shouldn't have led him down the wrong path, at any point. More intelligence should have been strictly superior to less. But if he wanted to get onto the right path, he should have been putting it towards figuring out what that path was, instead of coming up with cleverer and cleverer arguments, arguments that nobody could have stood a chance at refuting, for why he should have kept going exactly the way he already was.
And so, just as always, Dooku will hear what someone else says, and he'll notice that there is an obvious refutation, and he won't even think of doing the same thing to the point he just made.