Dartagnan and Porthos both lose their swords while chasing the Duke of Beaufort's carriage, but are seen wearing them again throughout the rest of the movie.
Whilst ballooning to the finale castle, the fire keeps changing from lit in long shots to unlit in close up.
When the Musketeers sit under the scaffold, Porthos fills his glass with wine and puts down the bottle. In the next shot, the glass contains more wine than Porthos had filled into it.
Cyrano de Bergerac's balloon is much too small to support the men it is seen to carry.
When Justine de Winter first encounters the Musketeers, she attempts to kill Athos with a pistol-sized crossbow but the bolt misses its target. She then fires again, this time the bolt knocking D'Artagnan's sword from his hand, but she is not shown to have re-drawn the cross-bow and load it and would certainly not have had time to do that in real life.
Cromwell is portrayed as leader of the Parliamentarian ('Roundhead') Army and de facto ruler after Charles I's execution. In 1649, however, he was still only second-in-command of the Army (he would not become commander-in-chief until well over a year later, following Sir Thomas Fairfax's resignation). William Lenthall, as Speaker of the House of Commons, was the nearest thing the new English Republic had to a Head of State until Oliver Cromwell took up the reigns of power as Lord Protector in 1653.
Balloons (both hot air hydrogen) were invented in 1783, 122 years after the death of Cardinal Mazarin.
In a scene in Justine's bedroom, a truck can be seen trundling across the road outside of her window.