During the Christmas party near the end of the movie, an outside view of a beautiful building is used as a location of the event. This building is actually located on the other side of the world, in Europe. More precisely in a small town called Tartu in Estonia.
There are no snow-covered mountains anywhere in Wisconsin.
When Emmett and Nell were cutting the Christmas tree, the safety cover was left on the axe blade. Then, when the tree was brought into the house, the base was clean cut as if it were done with a saw rather than an axe.