Bartok the Magnificent/Fridge

Fridge Brilliance: During Ludmilla's Villain Song a rat takes a sip of the potion and turns dragon-like itself. This may seem like a mistake, and maybe it was, but if Baba Yaga expected Ludmilla to steal the potion and drink it herself, then maybe she purposely made it a "turn into dragon" potion instead.
Fridge Horror: The Prince doesn't seem like the type to send people to the dungeon. Especially a dungeon with torture devices. So we're left to assume that Ludmilla is behind all those men being there. Just think of the amount of people she must have imprisoned and/or sentenced to death for asinine reasons.
- Don't forget that having a prince implies this movie was set before the events of Anastasia. So after saving Moscow from the dragon, Bartok went on to work for a holy man who was actually a fraud and...wait. Uh-oh.
Fridge Logic: What was the point of Ludmilla getting someone to dress up as Baba Yaga and drop the iron tooth when kidnapping Prince Ivan? Ivan was the only witness. She could have just kidnapped him normally and still said Baba Yaga did it.
- Maybe in case the Prince yelled loud enough, someone might check the tower, so she had him think it was Baba Yaga too...or she's aware of the fourth wall and wanted to attempt to fool the audiance, forgetting that her own acting is terrible.