Factual error: A toy modern four-door automobile and a clear plastic ball can be seen as the children play when the Burgermeister comes in on his wheelchair. Both unlikely for a story set (presumably) in the 1800's, at the latest.
Factual error: During Kris' "A Kiss a Toy" musical number, one of the kids has a Tommy Gun. Since the story is, at the latest, set during the 19th century and the Burgermeister's troops are armed only with spears, swords, and knives, a Tommy Gun should not be in this story.
Visible crew/equipment: When Kris is singing "Put one foot in front of the other", he opens a door through the snow and walks through it. If you look inside of it you can see a staple holding the two set pieces together.
Continuity mistake: When the Winter Warlock's icy heart melts, he is holding a toy locomotive with its front showing, but the next shot shows the locomotive's rear showing.
Continuity mistake: When Kris gives the children toys, one of them says, "What about the Meisterburger?" Kris than says, "What about him? I'll save him a big red yo-yo!" and pulls out a red yo-yo. However, when he hands it to the Meisterburger, it is not red, but is yellow and has blue and red stripes.
Visible crew/equipment: Whenever the Meisterburger talks, you can see the mouthpiece moving on his face.
Visible crew/equipment: When Chris and Topper are captured by the Winter Warlock's trees, before Winter Warlock appears you can see a crew member's hand holding an old style camera with a flash bulb, used to make the flash effect.
Continuity mistake: Meisterburger has a cast. Then he is walking without a cast. Then he has a cast again.
