Just before the Musketeers charge the castle for the final fight scene, d'Artagnan is seen in his normal clothes, then in his father's tunic, then once again without the tunic.
Some shots during the final battle show rain, while others do not.
When Planchett throws the explosive up on the platform where the enemy men are, it lands in front of one of the men's boots. In the next shot the explosion is behind them.
During the fight at the castle, D'Artagnan is fighting multiple guards while hanging from a rope. At one point, he slides down his own rope and is clearly seen dropping his sword. However, when he climbs back up, he resumes the fight with a sword in his hand.
The sky changes from overcast/gray to cloudy with blue sky during one of the carriage chase scenes. (This is the same scene where the jet contrails are visible)
Due to its granular nature, gunpowder of the period was highly susceptible to moisture. Once even a tiny bit of moisture got into any amount of gunpowder, it was very difficult to ignite, even impossible. Therefore it is highly unlikely that any of the muskets, pistols, or cannons used in the final battle would have fired.
Modern terms like "kilometres" are used by 17th-century characters. We are hearing a modern translation of what was "really" said.
The swords carried by the majority of the characters are rapiers and, as such, are thrusting rather than slashing swords due their relatively thin blades and narrow profile. There are multiple scenes were the sword is shown to kill opponents by slashing them across the chest which would have caused a lacerations, but not mortal wounds.
During one of the chase scenes, tire tracks are clearly visible in the mud.
The final scene takes place at the palace at Versailles which was not around when Louis XIII was king. It was built by Louis XIV.
The fighting styles shown resemble Asian martial arts more than European combatives of that era. It would have been at least 200 years before the Northern Europeans would trade with China and their arts became known in the West, It wasn't until after WWII in the 1940s that Westerners adopted their fighting styles en masse.
Exploding artillery rounds were not used until around 1785.
There are two jet contrails in the sky at D'Artagnan's parents' funeral.
In one of the carriage action sequences there are jet contrails, and a jet visible in one shot.
When d'Artagnan scales the tower wall, heavy foot steps are heard when he's only scraping his toes against the wall.
In the first swordfight, when D'Artagnan leaps and flies across the room to face the other swordsmen, the harness holding the actor in the air can be seen.