When the sheriff punches the mayor there doesn't seem to be enough snow on the ground .
The "12 Days of Christmas" actually start on Christmas Day (December 25th) and go through to January 5th. It is a common misconception that they start on December 14th and lead up to Christmas Day.
When Sam Fullard goes to the Frenchen's house you can very clearly see the daughter blink before the camera focuses on her face.
The Mayor would not be able to fire the Sheriff as he is an elected official and answers to voters.