The Addams Family Meet the VIPs - S1-E11
Revealing mistake: As Morticia and Gomez throw the knives at the target, and they stack tip to hilt, we can see the wire they slide on.
The Addams Family Meet the VIPs - S1-E11
Revealing mistake: After Mr. Harris leaves the play room, Fester goes to lay down on the bed of nails. As he does, the squared outline of the board under his robe he lays on is visible.
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.
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.
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.
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.
Morticia, the Breadwinner - S1-E26
Continuity mistake: As Pugsley tells Wednesday about satisfied customers, his arms are by his sides, then suddenly crossed.
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.
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 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.
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