In real life, Olga really did say that Anastasia's drawing looked like a pig riding a donkey. This was stated by Anastasia in a letter to her father, and the image used in the movie is a reproduction of the original picture.
The Parisian bridge, on which the confrontation between Rasputin, Dimitri and Anastasia occurs, is the Alexander III bridge, named after the real Anastasia Romanov's grandfather, on the occasion of his state visit to France in the 1870s.
The real Anastasia once wore a dress almost exactly like the one Anya wears in the last scenes of the movie. This same dress was seen in Anastacia, a Princesa Esquecida (1956).
The music box in this movie existed. It was given to Anastasia by Marie Feoderovna for her thirteenth birthday, but was silver, with a ballerina on top.
The portrait in the ballroom of the whole family includes a spaniel. The spaniel existed. The spaniel, named Joy, belonged to Anastasia's brother, Alexei, and was found alive at the house where the family was killed. Anastasia's own dog, Jimmy, did not survive.