Anastasia's hair kept changing from chest length to hip length.
There is no mention of Anastasia's two older sisters, Maria and Olga.
Anastasia is repeatedly called a princess throughout the movie. This is untrue as she and her sisters would be known as Grand Duchesses.
Anastasia is shown to be at least 5-7 during the Russian Revolution. At the time she was actually 17 and 29 days old.
Anastasia did not survive but in fact died with the rest of her family.