Other mistake: Near the beginning, Scrooge leaves Scrooge & Marley and walks home. As a result Bob Cratchit and the book keepers clean up and Bob Cratchit locks up with a key. Yet the next day when Scrooge gives gifts to the other book keepers, not only is Scrooge able to get inside without a key, the door is unlocked as well. (00:16:45 - 01:16:05)
Revealing mistake: During the ghost of Christmas present, Kermit is walking with tiny Tim on his shoulder and you can tell Kermit is walking on a spinning drum. Right before the camera pans away you can see Kermit's feet slide like he stopped walking but the road kept spinning. (00:55:00)
Continuity mistake: When Scrooge is talking with Honeydew and Beaker at the end, the Grapes Tavern sign behind them keeps changing position between shots. (01:14:30)
Revealing mistake: When Rizzo falls down the chimney and lands on the goose at Bob Cratchit's house, he burns his feet. When he is next to Gonzo, his feet are smoking. If you look closely, you can see the holes in the puppet's feet where the smoke comes out.
Audio problem: The ghost of Christmas past says "these are but shadows... they are what they are - do not blame me." Her mouth keeps moving after she stops speaking.
Suggested correction: No, it doesn't. When she finishes this speech at 45:16, there is an immediate cut to Scrooge. We can only see the back of the ghost. Her mouth is not visible.
Suggested correction: A mouth can move without speaking, not an audio problem but a puppeteering problem that is not a mistake.
A puppeteer problem would still be a mistake.
Maybe for the puppeteer, but in the movie it is no problem because a mouth can move without sound coming out. So what exactly went wrong?
But practically speaking people (or puppets) don't just flap their mouth open and closed with no reason. The overwhelming probability is simply that there was a dubbing error or a line was cut and the dialogue didn't fit with the mouth movement.
The mouth opens 1 extra time. That's all.
But it's glaring enough to be noticeable. Regardless of how or why it happened, it's a mistake.
In the version on Disney+, there is an immediate cut to Scrooge as the spirit finishes her speech. We only see the back of the spirit's head. Are you seeing something different on other versions?
https://www.youtube.com/watch?v=hBDqCFyugW0. I got the scene right here, it's at 1:50. Judge for yourself. I can repeat that part over and over again, but to be honest, sometimes it looks like there is an extra movement. Sometimes I can't see it. Even if it was, muppets move their mouths without speaking all the time.
Continuity mistake: When the song about Ebeneezer Scrooge is about to end, just as Ebeneezer is walking down the last lane, the first Muppet you'll see to the left when he has come down the stairs is wearing a red weird hat. Just a second after Scrooge has walked past the lady with the funny hat, when they sing, "If being mean's a way of life you practice and rehearse," you see the same Muppet with the same hat, now standing in front of Scrooge. She had no time to get there between the two shots.
Revealing mistake: As the ghost of Christmas present is finishing "It feels like Christmas", the camera starts to crane up. Look to the far right. The forced perspective effect starts to become noticeable with the background row of buildings. There are people that are slowly walking down that street and you can tell they don't get smaller as they should. Director Brian Henson said they were hoping people wouldn't notice the error.
Visible crew/equipment: During the final song, while they're all at the dinner table, there's a crouching puppeteer with a blonde ponytail next to the rats.
Continuity mistake: After the penguins ice skate, Gonzo and Rizzo skate, and Rizzo falls inside a barrel. If you look closely, you'll notice that Rizzo falls past the barrel hole.
Deliberate mistake: Gonzo and Rizzo are selling apples in the beginning, including the Red Delicious cultivar. That wasn't invented until the 1880s and the story is set sometime in the first half of the 1800s. Most likely intentional as they are the narrators.