Continuity mistake: Before this episode (and after as well) Darrin and Samantha give their address as 1164 Morning Glory Circle, however in this episode, when Darrin slams the door, the '9' in 192 on their address spins around to make 162, hence the angry neighbor at 162 saying that his grass was installed at the Stevens' by mistake.
Plot hole: Mrs. Kravitz, while standing in the Stephenses' front doorway, sees Santa Claus and assumes that it's Darrin in costume. However, the very next shot shows Santa exiting the kitchen (around the corner from the front door) and starting up the hallway toward the living room. There is no possible way Mrs. Kravitz could have seen him when she said she did. (00:09:30)
Revealing mistake: The hallway that leads to the den and the back door of the kitchen has a door at the end of it, when this door is opened we see what looks like pine trees and mountains, we know that the Stevens have neighbors on that side of the house, so that when the door is opened you can blatantly tell that it is a picture.
Revealing mistake: Darrin casts a shadow revealing painted sky background when he goes out to pay cab. Later, when he goes out to get in helicopter the neighborhood is not the neighborhood we normally see outside the Stevens' house. There's an Amoco gas station across the street.