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 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.
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.
Morticia Joins the Ladies League - S1-E6
Continuity mistake: As Pugsley comes out of the closet counting his money, he's dropping coins from his right hand to his left. A second later, it's reversed, and his facial expression changes in the same moment.
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.
Continuity mistake: As Fester gets a pistol from the drawer, there is an assortment of items in the drawer, and he leaves it open. A moment later, he goes to exchange guns, the drawer is closed and suddenly bare, except for the other pistol.
Continuity mistake: As Fester talks with Gomez, he has a fork in hand that has a small chunk of meat on it. In one quick take, there is an entire meatball on it, then a moment later, it's a small bite again.
Continuity mistake: As Fester talks with Gomez, he puts the fork with hamburger on it down in the bowl he's holding, and his right hand under the bowl. A second later, he's suddenly holding the fork.
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.
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.
Morticia, the Breadwinner - S1-E26
Continuity mistake: As Pugsley tells Wednesday about satisfied customers, his arms are by his sides, then suddenly crossed.
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.
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