There's nothing wrong with ambition. Really, we wouldn't get much done without it. In the case of The Count of Monte Cristo, though, the ambition in question would more accurately be called over-ambition. Most of the characters are overachievers, but not in the annoying but harmless teacher's pet kind of way. No, these overachievers are so driven that they're willing to do just about anything to get what they want. This doesn't just apply to the Danglarses and the Fernands of the world; Edmond is just as set on getting what he wants, when he wants. He's one of those guys who thinks "impossible" is just another word for "challenging."
As far as Dumas is concerned, ambition is a dangerous commodity, as addictive as any drug and as destructive as hatred and envy.
By the end of The Count of Monte Cristo, we find that ambition is a necessary, if destructive force, just as essential to human activity as air or water.