There is snow on the ground when Christina leaves the palace for the last time, yet there is no snow in the hills where Antonio and Magnus meet to duel nor is there snow at the docks where Christina boards her ship.
Christina signs some reports, moves a stack to her right, then hands a stack to the treasurer. The first stack disappeared.
The stagecoach wheel is shown bouncing out of a hole before it gets stuck.
When being crowned, the Chancellor is to the right of the throne, then is further away, then steps up to the young queen twice.
Christina is depicted as loved by her people. The real Christina, however, was, by the end of her reign, unpopular due to her arbitrary and wasteful ways, and having her royal historian and his son executed for accusing her of serious misbehavior and being a Jezebel.
Numerous historical liberties were taken for dramatic effect, especially the romance between Christina and Antonio, which never happened. The real Antonio Pimentel brought his wife and children with him to Sweden from Spain after he was appointed ambassador.
In the 1600s, in a remote, snowbound, humble inn, Christina is eating grapes and fruit that would not have been available even in the major, more southern cities like Paris.
The body of King Gustavus Adolphus was found at least two hours after his death by a gunnery which spotted his horse. After being separated from his riders and wandering behind enemy lines, he was stabbed once and shot three times, including a fatal bullet wound to the temple suffered after he went down. He had no "final words", as he does in the movie.
In the famous final shot, the wind blowing Christina's (Greta Garbo) hair is moving in the opposite direction from the wind that is powering the ship's sails. This was no doubt deliberate, as to have done it correctly would have meant her hair would be blowing across her face.
Christina's musket pistol did not make a cloud of smoke.