When they put on Nat King Cole to decorate the tree, the label is clearly RCA, and he only recorded on Capitol. Also, after part of only one song the album is over.
When alerting the community to save McHenry's, they passed out flyers and hung them. They hung a flyer with tape on a snow-covered tree, which is not possible.
When Lucy and Peter leave the fishing hut, the next scene shows a clock tower at 2:55, with a black sky that would mean AM, but the following scene is early evening at the tree lighting. It was afternoon at the fishing hut, suggesting that it's 2:55 PM. The sky should still be sunlit, not pitch-black.