When Anastasia goes to the Russian ballet, she is wearing a navy blue dress. However, throughout the scenes of the ballet, Anastasia's dress changes color from navy blue to a purple to a dark shade of red.
I found what this person is talking about. At the end when they have the credits, it shows the scene before they go into the ballet, and the dress is a deep red color.
She's at the ballet, the colors of the lights change causing her dress to look different colors. Oh, and it's really only different shades of blue not red or purple.