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Factual errors
For clarification, some swords were known as "thrust and cut" weapons. However, the swords used in the film, with the exception of Porthos', are designed purely for thrusting. The sharpened edges on the blades that appear in certain scenes were designed historically to help the blade get through tough material (like leather) during the thrust. These facts result in some rather direct mistakes in swordplay in the film. In particular, the final duel between Rochefort and D'Artagnan shows many errors. For a key example, during this duel Rochefort attempts several times to attack D'Artagnan by sweeping his rapier in a downward or sideways ark as if to slash him. In reality, the swords used lack both the weight and rigidity to inflict more than a superficial surface wound.
Milady discovers the razor-sharp, high-tension wires protecting the jewels by throwing a ribbon in the air that is cut in multiple pieces. As she does acrobat movements to work around the wires, she also cuts pieces off her own dress. As she reaches the end, there are no pieces on the floor behind her.
When Athos and D'Artagnan first cross paths in the market and talk, the position of D'Artagnan's hat changes repeatedly between shots.
The airships depicted, even if they had been feasible in the 17th century, in reality would never get off the ground due to their weight. Airships had to be of very light construction to fly (no cannons, etc.) The airships in the film were lifted by streamlined hot air balloons, so fire did not present the issues that Hydrogen would have.
The plot is set to happen between 1625 and 1628, which makes the umbrella ("portable device designed to protect a person against rain), a French invention dating from the 18th century impossible to have been used.
When D'Artagnan is shown entering Paris, he crosses a bridge over the Seine to the rear (south) of Notre Dame Cathedral. In the movie, the Seine appears to be extremely wide at this point (100's of yards on either side of Ile Saint-Louis - the island to the south of Notre Dame). In reality, the Seine is <500m wide at this point, and the islands are the majority of the width. The two water channels are extremely narrow to either side of the islands.
Airships are propelled by sails in the movie. This is impossible, as a hot air balloon can only travel as fast as the wind carrying it. The only way to move them would be with a mechanical device such as propeller.
During the flight from England back to France, the hair of The Musketeers is floating in the wind. As airships (similar to hot-air-balloons) are traveling at the speed of the wind, the people on board should experience this as complete calm.
Rapiers did, in fact, have sharpened edges. They are stiff, strong swords capable of slashing though, although not as good as "cut and thrust" swords. And even a slight slash can disable or distract, allowing for a killing thrust.
Buttercup's (the horse) spots start to run when he starts to sweat.
When the airship first appears, she does so flying low coming from behind the palace. Yet, in the panoramic view before Buckingham's arrival the whole horizon has almost no clouds, and the airship is nowhere to be seen, when she should be seen approaching.
During the vault scene, when the explosive charge on top of the lamp is lit, an electronic candle consisting of what appears to be many LEDs can be seen.
Milady de Winter (Milla Jovovich) points a flintlock pistol out of her carriage at Athos (Matthew Macfadyen) but the hammer holding the flint is in the half-cock position. This is the "safety" position and the pistol cannot be fired. This situation is covered by the famous old adage "don't go off half-cocked." In order for this to be a real threat the hammer would have to be pulled back to full cock.
(at around 1h 20 mins) Two of the musketeers turn to leave a brush past the ship's wheel. The whole structure, supports and all, wobbles backwards and forwards showing it to be a very flimsy prop.
The Spire on top of Notre Dame which impales one of the airships, was not built until the 1800s. The Church was restored starting in 1845 lasting 23 years, it was during this time that the Spire was added to the building.
The Cardinal and Milady are having a discussion in the Hall of Mirrors located in the Palace of Versailles. Versailles is outside of Paris and the hall of mirrors wasn't constructed until the third building campaign of the palace starting in 1678 by King Louis XIV.
In Venice, Porthos causes a flood by blasting into the canal with sticks of dynamite, which was invented in 1867 by Alfred Nobel.
In the ball scene, when the musicians are tuning their instruments, they are using Tourte bows, a style of bow that was not created until the late 1700s, significantly after the movie takes place.
Some scenes show Versailles. The "Three Musketeers" takes place during Louis XIII's reign. Versailles was not build before Louis XIV's reign, circa 1660. Louis XIII died in 1643. Should have shown the Louvre instead, in Paris (without the pyramid, of course).
When D'Artagnan is shown entering Paris, he crosses a bridge over the Seine to the rear (south) of Notre Dame Cathedral. In the movie, the Seine appears to be extremely wide at this point (100's of yards on either side of Ile Saint-Louis--the island to the south of Notre Dame). In reality, the Seine is 500m wide at this point, and the islands are the majority of the width. The two water channels are extremely narrow to either side of the islands.
Louis XIII's palace is obviously supposed to be Versailles (from the look of it and the interior scenes from the Hall of Mirrors), but an aerial shot places it at the site of the Louvre. Louis XIII did indeed live at the Louvre, but it didn't look anything like the palace in the movie at the time the story is set. The court moved to Versailles during Louis XIV's reign.
As the scene transitions from Meung Sur Loire to Paris, the map zooms from Meung Sur Loire to Paris. Based on the orientation of Notre Dame Cathedral, Meung Sur Loire would need to be to the north of Paris, when it fact it is to the south, though this map be a "deliberate" error by the filmmakers, since the alignment of the Seine in the map bears little to no resemblance to the actual geography of the Seine in Paris.
In the opening scene, the map of Europe botches the location and names of several German states. The label for Mecklenburg should be placed in the territory between Brandenburg and Denmark, the label for Ansbach should be placed in the territory between Saxony and Bavaria, and Münster should be east of the Netherlands where Brunswick is labeled. In general, the map of the states of the Holy Roman Empire and their borders is largely wrong.
As the scene transitions from Meung Sur Loire to Paris, the map zooms from Meung Sur Loire to Paris. Based on the orientation of Notre Dame Cathedral, Meung Sur Loire would be to the north of Paris. In reality it is to the south, though this map be a "deliberate" error by the filmmakers, since the alignment of the Seine in the map bears little to no resemblance to the actual geography of the Seine in Paris.
During the airship battle both sides aim for each other's decks rather than the far larger and more vulnerable air balloons themselves.
In the chess game, Richelieu suggests castling. In the standard rules of chess, this is not allowed when in a state of Check, or if King had moved in any way beforehand.
When the Cardinal's Guards chase after Constance at the port of Calais, one of their hats blows off.
(at around 1h 1 min) Just after "D'Artagnan--get after him!" the rider in the center of the frame loses his hat and it falls to the ground behind him.