The first card Andy opens shows a snowman with packages piled high. Barney then opens an all-white card from prison while Andy opens a card with Santa driving a Model-T. A few moments later, Barney opens an identical snowman with piled packages card. The camera angle changes. The snowman card is back in Andy's hand while Barney holds a previously unseen card of Santa before a hearth. As the camera changes again, the card in Andy's hand disappears, then reappears when the camera changes back. As Andy talks, Barney opens another envelope with Santa driving the Model-T card inside, but as they talk it changes into the all-white card from prison.
When Aunt Bee shows her deputy's badge, she does so by lifting the waist of her dress to show the badge underneath. When seen in the next shot, she is wearing an apron that didn't appear previously.
A close-up of the Christmas card from the Hubacher brothers says, "Greetings from State Prison." However, in the next shot, Andy reads it as "Merry Christmas from State Prison."
Some deciduous trees can be seen outside that still have their leaves. At Christmas these trees would have lost all their leaves for winter.
Ben Weaver is upset that Sam Muggins is moonshining because it competes with his "spirits" sales in his department store. Liquor in North Carolina can only be bought legally in state owned ABC stores, not in privately owned businesses.
After Andy tells Ben he has made Ellie, Aunt Bee and Opie his new deputies, they all show their badges. Ellie and Aunt Bee have badges that read "Mayberry Deputy," but Opie holds up a badge (upside-down) that says "Mayberry Sheriff." EDIT: Perhaps producers knew he had the wrong badge (not enough in the prop department for a one-shot?) and had him hold it upside-down to make it next to impossible to read on a 1960 television, but more likely it was a sly visual comment that Opie couldn't yet read.
When Andy is talking to Aunt Bee about Christmas Eve he tells her that "Elinor" is bringing the egg nog. Elinor is the name of the actress (Elinor Donahue). EDIT: The character is named Ellie, but her full first name is "Elinor," as seen on her diploma hanging in the drugstore.
Though people are wearing coats outside due to the cold, Andy's barred jail cell windows are without glass.
Ben Weaver exits the courthouse front to walk around the building counter-clockwise to the jail cell windows, keeping the building to his left. He passes the front corner of the building, walks around to the back corner of the building, then walks into the alley behind the building, all the time keeping the building to his left, but when he walks up to the barred jail cell window to look inside, he comes to it from a clockwise direction, with the window on his right, a mirror image of what it should be. This also creates another problem as, from the front, the courthouse appears to share a wall with the barber shop next door. As the cell in question lies opposite Andy's desk, there shouldn't even be a window in it unless it exists to allow prisoners to look in on men getting their hair cut.
When Ben pulls himself up to the courthouse window, the supposedly steel or iron bars bend a little.
There are three different calendars seen in the courthouse. The first shows 31 days with the 1st on Tuesday. That would make it March, 1960 or August, 1961. The second (behind Andy's desk) shows 31 days with the 1st on Thursday. That would make it December, 1960 (the month this episode aired). The third (in the jail cell) shows 30 days with the 1st on Monday. That would make it June, 1959 or April, 1963.
When the camera pans to Ben Weaver outside the courthouse looking in, as Andy and Ellie are singing "Away in A Manger," a calendar hanging in the cell shows Christmas falling on Wednesday. Christmas in 1960 fell on a Sunday. The most recent year on which Christmas fell on a Wednesday was 1957.
Andy tells Aunt Bee he hopes she made that good orange dressing like she did last year, but this is Aunt Bee's first Christmas in Mayberry since Opie was born.
When Aunt Bee shows her badge at her waist, the left hand can be seen wearing a wedding ring on the ring finger, but Aunt Bee was never married. The person portraying Aunt Bee in this scene is also slimmer than Frances Bavier.