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.)
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.
When M. Bonacieux is in the Bastille and a torturer places a roasted potato for him to unknowingly sit on, it is placed in a bowl in a close up but in all the long shots, it is on a flat plate.
Athos, wounded on the right shoulder, tells D'Artagnan that he fights equally well with his left hand. A minute later, he fights the Cardinal's men right-handed.
When Athos is hitting a Guard with a stick in the climactic scene at the palace, in one shot his sling falls off, but in the very next shot it is back on again.
When M. Bonacieux 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.
When the king is playing chess with animals as chess pieces, he commands one to move to the position of Knight 4. That should be in the second row from the left or right, but in fact the animal moved to the last row.
When Dartagnan rents his new room at Paris, it is possible to see at the stairs very modern glass bottles.
When the ship carrying D'Artagnan and his manservant is seen 'sailing' into Dover it is clearly being towed and not under its own sail, as a taut rope is pulling the front of the ship towards the camera.
During the fight in the convent, a branch is used to defeat an opponent, however it "snaps" before and then during the final blow. It clearly is a fabric prop despite the best efforts of the sound effects to disguise that fact.
When Constance thumps the Queen's writing-table with her hand and knocks over the inkwell, the inkwell actually begins tipping over before she even touches the table.
Just before the fight with the Cardinal's guards, Porthos picks up a large rock to use as a weapon. As he examines the rock, you can see that it's artificial, because he exposes the mould line.
Richelieu refers to Buckingham as the Prime Minister of England. However, the title was not adopted until the early 1700s, and even then was an unofficial name for the First Lord of the Treasury. It was not until 1937 that it was enshrined in law as the title of the Head of Government. Although Buckingham was undoubtedly one of the most powerful members of the English Court, he had no formal position as such, as there was no equivalent of a Prime Minister: the King himself was regarded as the Head of Government as well as Head of State.
When the crowd disperses after the Cardinal's procession, a little girl can be seen blowing bubble gum. Bubble gum was not invented till 1928.
During the first duel with the cardinal's guards that takes place in the convent, Porthos (Frank Finlay) goes behind a piece of laundry to hide from (and surprise) his opponent. From off-screen a crew member can be heard to yell "FRANK!" Then Finlay comes out from behind the laundry to hit his mark and finish the scene.
D'Artagnan begins to read a magazine in the office of the Chief Musketeer. But later he tells Buckingham that he cannot read.