Always Save the Girl: Double Subverted. D'Artagnan is initially willing to sacrifice Constance, saying their mission to save France is more important. Athos encourages him to save her so he doesn't become a lonely and bitter man like him after he lost Milady.
Avoiding The Great War: This film contains perhaps the earliest example of this trope as far as the time period goes. The villains were trying to start a war among the empires of Europe. While the dialogue focuses on the continent, the idea is still the same, not to mention that a war of the European powers at the time would have likely included colonies in Asia, Africa, and the Americas.
Bare-Handed Blade Block: D'Artagnen blocks Rochefort's sword with the back of his hand and later catches it. Both feats leave his hand bloody.
Batman Gambit: Richelieu's makes up the plot, so the Musketeers counter with their own Kansas City Shuffle; Milady knows what they'd normally do, and they know she knows, so they decide to send D'Artagnan in as a decoy to get Buckingham cocky enough to let down his guard so the other musketeers can steal Buckingham's Cool Airship, which they can then use to kidnap Milady, who sure will have the jewels they need because she would never trust anyone else to keep them!
Elite Army: This version takes this and the Praetorian Guard aspects of the Musketeers played up in other movies Up to Eleven so that they're essentially royal Special Forces. Also the three Musketeers make up the entire corps, until D'Artagnan makes four.
I Know You Know I Know: The break-in at the Tower of London takes this to amusing levels. Milady, who's worked with them in the past, knows their methods, and can give Buckingham the information. They know she knows their methods and will tell Buckingham. She knows they know she knows and will tell Buckingham. The English capture D'Artagnan, who she knew they'd use to infiltrate while the others acted as decoys, assuming she wouldn't take him into account. Turns out, they knew she'd do that, he's the decoy, and they do something completely different.
Large Ham: Orlando Bloom quite clearly is having a grand old time. Then again, much of the cast looks like they're having a lot of fun. Even Milla, of all people. Intriguingly, Christoph Waltz averts this as Richelieu, a historically prize ham role.
It could be argued that the accents are a translation convention. Most Parisian characters speak in Received Pronunciation English accents, while D'artagnan, a Gascon has Logan Lerman's American accent, as does his father, despite his being played by British actor Dexter Fletcher.
That's also used for creation of illusion that Milady and Constance were Spared By Adaptation cause Constance dies after the beginning of the war with England and Protestants and Athos needs an unsuccessful attempt in killing Milady to justify her execution. Pragmatic Adaptation meets Sequel Hook.
Razor Floss: Part of the security measures in Queen Anne's safe.
Refuge in Audacity/Crazy Awesome: You're being hunted by the Cardinal's men in an airship that, whilst it is cool, is also sinking a bit. What are you gonna do? Why, crash the ship into the Palace gardens, present the King with a document the Cardinal wrote himself which, out of context, makes the Cardinal seem loyal to the throne, making it impossible for him to actually do anything against you without revealing his own dirty work, of course!
Anderson is a fan of the 1973-74 two-part version directed by Richard Lester. Like those films, D'Artagnan is introduced sparring with his father, Athos wears all black, and Rochefort has a red outfit with an Eyepatch of Power.
What If?: Done with gusto. Athos as bitter at state ex-MIB leads to the whole new attitude towards women - like lecturing D'Artagnan that saving your true love and enjoying the youth is better that having your life ruined by serving the crown. Total opposite of the personality in book.