The pronunciation of Anastasia's name varies. She is announced at the ball as Anna-stay-zha, but for most of the rest of the first part she is called Anna-stahz-iya, which is closer to the correct pronunciation. Strange that a servant who worked at the palace for the royal family wouldn't know how to properly pronounce her name.
All the children are portrayed as being quite young at the time of their deaths. In reality, Anastasia was seventeen, Alexei thirteen, Marie nineteen, and Olga and Tatiana both in their twenties.