Morticia and the Psychiatrist - S1-E2
Continuity mistake: When Morticia is watching Gomez and the trains, at the second of the collision and explosion, it's a re-use of the shot when Mr. Hilliard is there, as in just a split second, you can see him, then there's Morticia again.
The Addams Family Goes to School - S1-E1
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.
The Addams Family and the Spaceman - S1-E27
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.
The Addams Family Tree - S1-E5
Audio problem: With Morticia in his arms, he says "And I dropped you...only once." If you watch his profile, you can see that his face never moves. Hard to believe especially when you know he had an animated face.
The Addams Family Goes to School - S1-E1
Audio problem: When Wednesday comes into the house crying her mouth isn't moving.
The Addams Family Goes to School - S1-E1
Audio problem: After Gomez suggests the rack for a stretch, he rings for Lurch. You hear Lurch say "You rang?", but his lips don't move.
Cousin Itt Visits the Addams Family - S1-E20
Revealing mistake: In the wide shot of the family watching Cousin Itt perform magic tricks, you can see Felix Silla's legs as they probably didn't intend for the whole character to be in frame.
Continuity mistake: While playing chess, and when Pugsley calls him, Thing is a left hand. When he comes up in the garden area, he's a right hand.
Uncle Fester's Illness - S1-E18
Continuity mistake: When we see Wednesday playing a game with Thing she is missing two front teeth. Later when the doctor comes to check on Fester she is only missing one front tooth.
Continuity mistake: After the doorbell knob retracts into the frame, the door starts to open. After the angle change, the door starts to open again.
The Addams Family Goes to School - S1-E1
Continuity mistake: When Wednesday is first holding her doll, the buttons are facing forward. A second later, it's backwards.
The Addams Family Goes to School - S1-E1
Other mistake: When Thing is first seen, he's a right handed thing. When Wednesday gets the mail from him, Thing is a lefty.
The Addams Family Goes to School - S1-E1
Other mistake: As Gomez and Hilliard come to the top landing, the supposed access behind Gomez at the top of the stairs can be seen to be either a blank wall or a door that should be a hallway.
The Addams Family Goes to School - S1-E1
Visible crew/equipment: If you look at the shrubbery, you can see the person performing our first glimpse of Thing moving around.
Uncle Fester's Toupee - S1-E31
Visible crew/equipment: As Gomez goes to ring for Lurch, the shadow of the boom mic is on the wall behind him.
Uncle Fester's Toupee - S1-E31
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.
Crisis in the Addams Family - S1-E24
Visible crew/equipment: In the play room, as Fester goes to leave, the shadow of the boom mic is on the wall behind him.
The Addams Family Meets the Undercover Man - S1-E16
Continuity mistake: After Conkey says "Yes, it is", in the long shot, he lowers his arm. As he goes to answer Gomez, his arm is suddenly up.
The Addams Family Meets the Undercover Man - S1-E16
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.
Wednesday Leaves Home - S1-E10
Other mistake: As Fester comes into the room where Gomez and Morticia are, the piece of the cactus leaf that Fester is to eat is differently colored than the rest of the leaf.
Answer: Basically from what I understand, they stuck the innards of a small flashlight into the base of the bulb and put a little switch on it. When he put it in his mouth and bit down, his teeth would hit the switch, which would turn on the flashlight and made the bulb light up.
TedStixon