The Count thinks of himself as an agent of Providence, but he's wrong, and in the end he realises it; in attempting to punish the wicked and reward the good, he also injures several of the people he set out to reward and does quite a bit of harm to innocent bystanders.
Valentine is the daughter of Villefort's first wife; the woman he's married to when the Count hits town is his second. It is heavily implied that Valentine's maternal grandparents, particularly her grandmother, are poisoned by the second Madame Villefort, who learned of poisons and was supplied with 'medicine' by the Count. Yet, they had caused Dantes no harm, and likely never knew he existed.
The motivation? Their fortune would go to Valentine; if Valentine died or entered a nunnery, her father would inherit. Then Madame's son would inherit from his father. This was also why Nortier was a target until he changed his will, and why he became a target again after he changed it back.
Nortier was also someone nearly killed by the Count's web of revenge, and he didn't know Dantes existed until after his imprisonment. Villefort didn't tell him how he found out about the information in the letter.
Albert is nearly killed in a duel by the Count, until Mercedes comes to plead for his life. (Mercedes is also implied to have pled with Albert as well for Edmond's.)
The Count coldly manipulates Bendetto's foster-father, who is in his employ. It's frightening in comparison to the kindness to his servants he normally shows, and illustrates just how far he'll go to get his revenge.
Bendetto shares a mother with Eugenie, yet the Count had no problem with them getting betrothed to further his plan. (Which heads into squick territory.)
Villefort, Ferdinand, and Danglers did deserve to be smacked upside the head six ways from Sunday for what they did in their lives, Edmond's framing being only one of their crimes, but the Count did not seem to care about collateral damage to undeserving (or completely innocent) parties as long as he got his revenge. This is why he's no agent of providence or any other force, but a very human man.
Edited by Candi Coming back to where you started is not the same as never leaving. -Terry Pratchett
Not about revenge. Instead, it is about Providence. Edmond Dantes arranges for those who did wrong to suffer, and rewards those who were good.
Villefort - His ambition perverts his job as a judge, and he ignores or hides crimes by his family. So the Count points his wife in the direction of poisons, knowing Villefort won't go to the police when she kills because of the shame.
Danglars - He greedily embezzles money from his clients, and uses insider trading. The Count arranges for him to receive false insider reports and ruins his investments by stock manipulation.
Morcef - Betrayed Ali-Pasha. The Count arranges for others to investigate and discover this fact. When he is publicly shamed and his son and wife leave him, he commits suicide.
Then the Count rewards Dante's friends:
Carderouse - Drunk during the betrayal, speaks against it, and laments that it happens when the Count (in disguise) probes about what happened. The Count gives him Edmonds "estate" and he F's things up from their himself.
Morrel - Saves his shipping business by paying off his debts and bringing in a restored ship.
The Count at one point even says that he sold his soul to become an agent of Providence, punishing the wicked and rewarding the good.
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