Revealing mistake: Samantha is standing with Serena when the the computer dating representative, John Fiedler, informs Serena that she has a date with Frank. As he enters the room to make his announcement, Samantha's back is to the camera but she turns slightly to her right toward the camera and you can see her face in almost full profile for a split second. It's obviously Samantha's double.
Revealing mistake: In addition to Samantha, Elizabeth Montgomery also played Serena. In scenes where both characters appeared, Elizabeth would face the camera and play one character and another actress, Melody McCord, would play the other with her back to the camera. But in this scene, Melody (portraying Samantha), with her back to the camera, inadvertently turns her head, revealing her face.
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.