While Zach and Mary are gathered at the Christmas dinner with the family, Mary hands a plate of the dessert to Zach, but in the next scene the dessert isn't in front of Zach.
When the boy throws his toy airplane at a little over 5 minutes in, at first you see Ginger Rogers with her face looking outside the window, looking slightly amused, and not holding up her newspaper; when the camera cuts to her a split-second later, she's holding her newspaper up as though she was still reading it all that time, and she looks a bit annoyed.
(at around 47 mins) Barbara turns on an old vacuum tube radio and Silent Night immediately begins to play without the radio warming up. Then she begins to turn the tuning knob a considerable amount, but the same song continues with no station change or static.
When Zach enters the house and Mrs. Marshall takes his coat, both his coat and his uniform bear the rank of a first sergeant with 3 stripes up and 2 down. When Spring hangs his coat in the closet, it has the rank of a Master Sergeant on it, 3up/3down.
When Zach calls Mary the first time, and Mary invites him to dinner, she gives him the address and says, "Don't be late," but she never tells him what time he should arrive. However, he still manages to show up exactly on time for dinner.
When Mrs Marshall hang's up Zach's overcoat in the closet, the rank on the overcoat is that of a Master Sergeant, but he is a Sgt First Class and not a Master Sergeant.
Mary tells the taxi driver the address is 617 North Elm Street, but on the phone she tells Zach the address is 617 Elm Street.