The best way to watch a movie is with suspension of disbelief - Just trust what the producers present you with and don't question it. With that, "Anastasia" is one of the most delightful movies I've seen in some time. It's like an old musical, with people spontaneously erupting into choreographed dance, but with modern dialog (And funny, at that!), an enjoyable romance, and action sequences to keep things moving. The music, while nothing to remember to the point of distraction, was perfect for humming, and even worked to advance the plot - Unlike so many animated songs put in for the sake of having a song. So it wasn't historically perfect - if it were, there'd be no story. Go ahead and feel smug that you know what really happened, but don't turn to comment to your neighbor, lest you miss one minute of the wonderfully unfolding plot.
