After receiving the information about the assassination from Lady De Winter, the four men are seen riding around shooting arrows to rally the other musketeers. In one shot (after which Athos' original white horse is killed) he is seen riding a brown horse. A later shot of all four of them have them all on the white horses again.
D'artagnon turns around to Gerard and says, "In the meantime, give my regards to your sister." He then turns back round and a red and gold-ish striped blanket is strapped to the back of the saddle which was not there before.
In the final fight scene between the musketeers and the cardinals guards, D'Artagnian is fighting the assassin. Porthos shoots the assassin with a crossbow from the ground and the assassin clutches the arrow in his chest and falls. As he falls, you can see that the arrow is gone.
During the fight between Athos and Rocheforte in the end battle scene, Rocheforte is wearing a sword sheath. Athos knocks him down, and when he rises to begin fighting D'Artagnian in the next shot, the sheath and belt are missing.
At the end, when Athos, Porthos, Aramis and D'artagnan are in their Musketeer gear, complete with light colored hats. When they give chase to Girard and his brothers, the light colored hats are separated. The first light colored hat doesn't come in until midway instead of all four being together at the start.
In the final fight between D'Artagnian and Rocheforte, D'Atagnian stabs Rocheforte on the left side of the row of buttons, five buttons down. We cut away to D'Artagnians face and in the next shot, the sword is on the right side of the row of buttons, three buttons down.
After Rocheforte knocks D'Artagnian out in the dungeon and tells the guard to "Take him below" the guard walks in and drops the keys and reaches for D'Artagnian but after the camera angle changes he clearly still has them in his left hand.
When D'Artagnan jumps down from the carriage to unhitch the horses, he throws the reins forward over the nearest horse's back. A few moments later Porthos grabs the reins which are now resting on the driver's seat, and throws them forward again.
Aramis is shown quoting Genesis (the first chapter in the Bible) while presumably reading from a Bible, which is open in the middle. Given Aramis' reputation and the subsequent action, it is possible that he was quoting from memory and merely had a book open in front of him to give the impression of piety.
In the final fight between D'Artagnan and Rochefort, after Rochefort has knocked D'Artagnan down the stairs, we cut to see him rolling. There are no stairs in this shot, he is obviously rolling down a ramp.
The goof items below may give away important plot points.
During the execution rescue scene as Aramis and Porthos assure D'Artagnan that his rescue is at hand, Porthos remarks that the axe was a "gift from the Tsarina of Tokyo." The Three Musketeers story takes place between 1625 and 1628, a full 240 years before the city of Edo in Japan is renamed "Tokyo" by the Emperor Meiji in 1868. Regardless of how far fetched Porthos' claims may be intended to be, there is no historical way he could have known the term "Tokyo," which means "Eastern Capital" in traditional or archaic Japanese.
When the cardinal shots Aramis,he falls to the ground,and Porthos runs to him. When Athos is there too, they discover that Aramis' cross saved his life,yet it is clearly seen that the cardinal shots him in his stomach and not upper, where the cross is hanging from his neck.