Continuity mistake: After Mr. Hilliard goes through gate and nears the house, it's really at the real house. A second later, he's approaching the now-familiar front porch on the studio set. This is easy to tell because the layout of the two porches are radically different.
Other mistake: In this episode, the radio announcer said that the reported spacecraft was seen over the Cemetery Ridge District, and Morticia said "That's our area." However, in "Cousin It Visits The Addams Family" (S1: Ep 20) they are supposedly in the Greenbriar Woodlawn District.
Other mistake: Bad editing shows up a couple times in this episode. Once when Max goes to ring the doorbell. As he reaches for it, it moves out and in on its own and he moves with it. As he does, its easy to see the film is run back and forth. The second time is when he reacts to the news of Kitty. He flinches, and his toupee slips over his face, then the film is run backwards so it goes back.
Audio problem: Ted Cassidy (Lurch) was an accomplished organist. However, when he "played" the Harpsichord, he was only miming the actions. When Lurch is playing while Gomez and Morticia are fencing the music doesn't match the movements of his hands.