The pronunciation of 'Athos' varies throughout the movie. Not only do different characters say his name differently, the same character - Philippe - pronounces it differently at different points in the movie.
When D'Artagnan arrived in the throne room immediately after realizing that something is awry, he nods to the King on his throne while standing on the far right of the King. When the camera shoots to Louis nodding back, he nods slightly to his left, even though D'Artagnan was just standing to the King's far right.
In the chapel when D'Artagnan finds Queen Anne crying she hugs him and moves his hair to his left shoulder. When he turns it is still on his left shoulder but after he calls her name it is divided evenly over his shoulders.
After rescuing Philippe, when Porthos and Aramis are sitting on the wall talking, Porthos' hat brim is up on both sides, when Aramis walks away and a bird drops a "gift" on Pothos' hat, one side of the brim is now down.
When the King asks Aramis to find and kill the Jesuit leader, a shot from the King's side looking at Aramis is followed by a shot from Aramis' side in which the King still looks straight ahead and only then turns his head towards Aramis.
At the beginning of the movie, we clearly see King Louis XIV inside and outside of the castle Vaux Le Vicomte. Louis XIV never lived in this castle, as it belonged to Nicolas Fouquet. Vaux Le Vicomte became a source of inspiration for the Versailles castle. Versailles was the living place of Louis XIV when he was old and is shown in the movie. Therefore, all castle sets are wrong, since the young Louis XIV lived mostly in the Louvre/Tuileries palace, in the center of Paris, not shown in the movie.
It's been pointed out that, since the twin brothers were not really fathered by Louis XIII, neither would have a claim to the throne and Louis would not be king to begin with. However, since the origins of the twins' birth was clearly unknown to any (excepting the real parents) in the film, including the twins themselves, this is highly irrelevant.
When D'Artagnan is dealing with the angry peasants about the spoiled food, and the apples are thrown, the second apple that D'Artagnan "stabs in the air" is visible on his sword before the slow-motion shot.
The goof items below may give away important plot points.
In the final scene where the Kings' guards form up to shoot the musketeers and Philippe, the click of cocked hammers is heard. However, the guards are using matchlocks, which are correct for the period, but they cannot make that sound. They would make no sound at all until fired.
Near the end of the movie when the musketeers fire upon the charging five, we see a giant cloud of billowing smoke from the guns. But the room is enclosed and there is no way for the smoke to dissipate quickly. But when Louis attempts to stab his brother, there is no smoke at all.
The closing narration says that King Louis XIV gave his country and subjects peace, good food and prosperity. This is not accurate: the reign of the Sun King began with a splendorous and hopeful "honeymoon" for the nation, but was then marred by many wars (first with the Netherlands, later with England), bankruptcy due to the massive costs of building and maintaining the Palace of Versailles, high taxes and popular uprisings over wartime food rationing. In the last years of his life, Louis XIV ruled over an impoverished, defeated and demoralized kingdom. In fact, the scandalous lifestyle of this king and his successors (XV and XVI) were the main catalyst of the French Revolution. In France, Louis XIV fashions and designs have remained popular, but the man himself is usually regarded very negatively.