Continuity: In some stunts, the musketeers are seen for short spans of time with no rapiers - their hands are empty, as are their scabbards, while before and after they wield their swords. (One notable example is d'Artagnan climbing the walls of the palace near the climax.)
Continuity: When Athos is hitting a Guard with a stick in the climatic scene at the palace, in one shot his sling falls off, but in the very next shot it is back on again.
Factual errors: When M. Bonancieux is using his periscope in the palace gardens, his view is shown as being upside-down. In fact a periscope does not invert the image.
Revealing mistakes: Just before the fight with the cardinals' guards, Porthos picks up large rock to use as a weapon. As he examines the rock, you can see that it's artificial, because he exposes the mold line.
Revealing mistakes: During the first duel with the Cardinal's guards that takes place in the Nunnery - Frank Finlay goes behind a piece of laundry to hide from and surprise his opponent. From off-screen we hear a crew member yell "FRANK!" Then Finlay comes out from behind the laundry to hit his mark and finish the scene.
Continuity: During the fight in the laundry, one of the Swiss Guard threatens Athos with a pole. The Guardsman is bare-headed but a moment later, when he attacks, he is wearing his hat.
Errors made by characters (possibly deliberate errors by the filmmakers): When in the beginning of the first fight in the Carmalite convent, D'Artagnan shouts at Porthos for a sword, calling him Aramis.