In the opening train sequence, Ben is sitting on the left side of the train when shown from the front, but sitting on the right side of the train when shown from the back (when Katie bumps into him).
When Ben and Katie meet on the train, they are seated across the aisle from each other. The train has both forward and rear facing seats. They have their left arms to the aisle then their right arms. The switching happens multiple times. He even extends his right hand to shake and the camera angle changes to show them shaking with their left hands.
The book the carolers are using is an actual well known book of carols. The carol they sing at Barbara's using the book is not actually included in it.
It was Charles Dickens who wrote "A Christmas Carol" which was first published in December of 1843. Not Louisa May Alcott! It did, however, inspire her to write a highly similar children's version called "A Christmas Dream" (which was published forty-two years later, in 1885).
The drawers in the time capsule have metal rails on the bottoms - which would not have been the case in a drawer from 50 years ago. Also in one scene, you can see the mayor close a drawer and it has a soft close feature - definitely something that would not be on a 50-year old piece.
None of the items in the time capsule are old. Also the top hat that was supposedly made in an old factory in town is brand new.
Near the end of the movie when they are making snowmen, it's obvious that the perfectly-round snowballs used are made of Styrofoam and not snow.
Katie needs a phone charger and goes to the Daisy's General Store to get one. Unless it is an universal charger because the type of phone is never mentioned or even shown.
At 01'18" into the movie, Katie is on the train and runs out of battery on her cellphone. Looking for a power outlet she stands up. In the next shot Ben is sitting on a seat at de left side of the train. When Katie arrives at the row where Ben is sitting the train shakes and Katie falls to the right against Ben's left shoulder, while Ben is now sitting at the right side of the train.
In the following shot Ben is sitting again on a seat at the left side of the train.
Katie mentions her surname is Connell, which is shown on her computer. In the end credits, her mother's surname is listed as McConnell.