Fandom Nod: Look closely, and you'll see little visual shout-outs to other movies from Don Bluth's history. (The squirrels look like they've walked right off the set of Sleeping Beauty, Bartok is sucked into Hell just like Charlie, there's a spooky thorn bush near the end that Brutus might be guarding, and so on).
History Marches On: Sadly, in the years since the making of this film, it has been conclusively proven by exhuming the graves and DNA tests that the real Anastasia was indeed killed by the Bolsheviks, along with the rest of the Russian royal family. However, the movies does seem to make a nod to the fact that prior to the making of it, the mystery surrounding the real Anastasia had yet to be cleared, because while she and her grandmother are reunited in the movie, the Dowager Empress Marie for some reason still narrates at the beginning that she "never saw my beloved granddaughter again."
What Could Have Been: In the film, Rasputin's reason for being evil is never really explained - he's briefly described as being a "fraud" and a "traitor", but nothing else - and it's the Tsar's attempt to expel him from court that leads to him swearing vengeance against the entire Romanov line. In the original drafts of the story, Rasputin only became evil after the relatives of the Tsar made an assassination attempt against his life - which historically killed him - and he swore vengeance after mistakenly assuming the Tsar had arranged it.
Rasputin also didn't drown and end up in limbo in these drafts; instead he escaped to the countryside in a travelling wagon, and only returned when he realised that Anastasia was still alive.
Vlad and Sophie were originally supposed to be dancing together in the opening scene, giving a greater insight as to how they know each other, and how they're connected to Anastasia's family.