Deliberate mistake: When the saloon patrons pour through the swinging doors in pursuit of Packer, the same people are seen repeatedly. A relatively small number of extras are running around to the rear of the set and re-entering through the back so that they will appear to be a larger crowd of people.
Deliberate mistake: When Swan sings "Let's Build a Snowman," the snowman looks like your basic run-of-the-mill snowman in almost all of the shots. However, there is one long shot where the snowman's head is much narrower, and looks suspiciously like the alien "visitors" from South Park. [If you watch the DVD with the director's commentary, Trey Parker and others admit to putting aliens in random shots of the movie. It is during the bar fight when they say this, right as a shadow of an alien is on the wall behind the actors. This was done on purpose.]