Revealing mistakes: When the bomb attached to the bread is thrown back at La Rochelle, it is the bread which explodes as the bomb is still clearly intact after the explosion
Continuity: After the Musketeers rescue Rochefort, he puts on his hat twice between shots.
Anachronisms: At the time movie takes place (early 1600s) firearms were either matchlocks or wheellocks, or flintlocks. So the musketeers and their rivals using matchlock muskets is correct, but Lady de Winter's percussion pistol wouldn't be invented until the 19th century.
Revealing mistakes: In the swordfight on the frozen river, the lumps of broken ice float high in the water like Styrofoam. Real ice would be 9/10 below the surface and water would slosh over the lumps as they were moved around.
Continuity: After the bedroom fight between D'Artagnan and Milady, in the café scene, when D'Artagnan stands up and accidentally drops a piece of jewelry on the table, Athos grabs D'Artagnan's hand with his right hand while his left hand is holding a pipe in his mouth. In the next scene, Athos is holding his left hand over D'Artagnan's, while his right hand is holding the pipe.
Continuity: During the fight at the burning building Porthos attempts to escape by performing a 'death slide'. When he begins the slide he clear had bare hands, when he finishes the slide (just before he sets himself on fire) we can see he is clearly wearing gloves.
Continuity: In the climactic duel in the convent, Rochefort's wound moves lower between shots.