Audio problem: The animated Christmas movie the boys are making is really "the Spirit of Christmas", the movie Trey Parker and Matt Stone made before South Park. The dialogue recorded by the boys is the same as in the original (with a few changes, but when the film is shown later it's the original speech from "The Spirit of Christmas". You can tell by the way the voices are done, and the tone of the voices.
Continuity mistake: In the town hall meeting scene, a man says that he is "shocked and appalled" by what has happened. In the wide shot, he is sitting next to Liane Cartman. In the closeup, Liane is replaced by a woman dressed in purple. In the next wide shot, Liane is back.
Continuity mistake: When Stan threatens to cut his hand off, you can see his wrist, but just right before he does it, his wrist disapears between his glove and jacket. If his wrist was showing, he couldn't have had his hand pulled inside his jacket and he obviously couldn't have done it while holding the meat cleaver.
Continuity mistake: At the beginning when Cartman is showing the old women the hippies in the attic, there is a pair of boots and some other things behind them. It does two shots that show the things behind them, then in the last shot before they leave the attic, all the things are gone. (00:01:10 - 00:01:28)
Continuity mistake: At the toy store, Stan shows Cartman the three Chinpokomon he is buying: Lambtron, Roostor, and Shoe. When Stan's mother is at the cash register paying for his toys, though, she has a different Chinpokomon and Pingin. At the bus stop the next day, he has yet another different Chinpokomon.
Continuity mistake: When the town are protesting outside the Mayor's office, the woman at the front of the Nativity protesting group is wearing a purple shirt. A few seconds later, she is with the group against the cutting-down of Christmas trees wearing a completely different shirt (white with a Christmas tree in a red circle with a line through it).
Plot hole: How was Cartman able to afford a fairly lengthy TV ad, when he had already spent all his money on the theme park? Cartman took all his money with him to buy the theme park. After buying the park, he runs the TV ad mocking Stan and Kyle. Soon after, when he hires the security guard, he reiterates that he had spent all his money to purchase the theme park. Cartman would not be able to get a loan (he is too young), even as a co-signer. Cartman's mother is also not wealthy enough to give him the money.
Continuity mistake: In the cemetery scene where Kyle calls the emergency hotline and Stan and Cartman hold off the zombies, in the shot where Kyle's hand holding the Worcestershire Sauce is shown in close-up, his gloves are shown as green instead of white, which they are while Kyle is in his vampire costume.