Antagonistic Offspring: Albert confronts Dantes, though neither of them are aware of the relationship at that time.
Anti-Hero: Edmund, as The Count, starts off as a Nominal Hero, only heroic at all because he's using his deplorable tactics to gain vengeance on the men who condemned him to false imprisonment. However he graduates to Unscrupulous Hero at the end when he remembers his mentor's words and offers Mondego the chance to leave with his life. He doesn't take it.
Beardness Protection Program: The Count trims his prison beard as part of his noble disguise. Noteworthy because of how effective it is. Upon returning to exact his revenge, Dantes is able to fool Villefort (who admittedly only met him once), his longtime employer Morrell and his lifelong friend Mondego. Only Mercedes recognizes him. Mondego actually doesn't recognize him til he shaves.
Call Back: How Mercedes realizes that the Count is Edmond, given his habit of twirling his hair.
Chess Motifs: Edmond and Fernand have a chess king that they trade back and forth when the other has a victory, recognizing the other as "King of the Moment". Edmond explains this to Napoleon Bonaparte, who observes that "In life, we are all either Kings or Pawns."
Hollywood Atheist: Dantes loses his faith on account of his unjust imprisonment (and then regains it at the end of the film). This is a contrast to the novel, in which Dantes is still religious as the Count — he just worships a very vengeful God.
Human Ladder: The priest asks to stand on Edmond's shoulders to see out a window for the first time in decades.
Meaningful Name: Abbé Faria ("The Mad Priest"). Notable in that since he hasn't had a conversation during the length of his entire sentence in the prison, he must have given this name to himself.
Modesty Bedsheet: Mercedes gets one. Justified in that she's concealing her naked body from the manservant of her lover, and not her lover himself. Averted in that once said manservant gives her favorable news, she suddenly cares not for preserving her modesty.
Number One Dime: A chess piece has sentimental value to Edmond and Fernand.
Physical Scars, Psychological Scars: The scars on Edmond's back that he received from being repeatedly lashed in the Chateau D'If represent how his time in prison embittered him.
Pragmatic Adaptation: Many aspects, including the relationships between major characters and the ending, have been changed, simplified, or removed; and action scenes have been added. The main themes of the story are intact. Given that this is an adaptation of a 440,000+ word novel, this is probably for the better.
Sarcastic Clapping: Abbe Faria does this when Dantes realizes the reason Villefort burned the incriminating letter and imprisoned him right after acquitting him of the charges.
Sauna of Death: A scene with Villefort and the Count takes place in one of these.
Spotting The Thread: Mercedes realizes The Count is Edmond when he twirls his hair the same way he used to.
Tired of Running: After Fernand shoots Mercedes, he turns tail to run, mounts his horse and escapes at full gallop. However, after less than a minute, he pulls up and takes a moment to stare at the horizon, remembers his station, turns around, draws his sword, and shouts his challenge.
Fernand: I couldn't live in a world where you have everything and I have nothing.
Took a Level in Badass: Edmond is a hapless, uneducated merchant sailor when he is arrested; he returns to Marseille as an educated, erudite, swashbuckling nobleman.