Revealing mistake: As Fester looks at the mirror, it shatters. After he asks a question, it falls off the wall. After it does, you can see what appears to be someone's fingers pushing from the other side to knock the mirror down. That spot on the wall is obviously fabric covering a hole.
Halloween - Addams Style - S2-E7
Continuity mistake: As Gomez and Fester bob for apples, the apples in Gomez's bucket alternate between swirling around and being still between close up and distance shots.
Morticia, the Sculptress - S2-E9
Continuity mistake: As Morticia tries to sculpt Lurch, the boulder she is working on gets a sudden vertical crack in it from the wide shot to the close up.
Visible crew/equipment: As Thing withdraws into the tree, in the wide shot, you can see someone's elbow pop out from the tree.
Revealing mistake: In the wide shots of the car, the camera side of the sound stage is reflected in the car's finish.
Continuity mistake: After talking to Cousin It, Morticia is reading a book titled "The Law of Bigamy." As the camera does a close up on the book, the label on the spine says "Homer's Iliad".
Christmas with the Addams Family - S2-E15
Other mistake: As Morticia starts to play the flute, Gomez appears to have been filmed backwards, his hair and suit is reversed.
Christmas with the Addams Family - S2-E15
Revealing mistake: When Morticia is playing the flute, the strings that operate the basket lid and rope are visible.
Christmas with the Addams Family - S2-E15
Continuity mistake: When the second Santa (Grandma) knocks at the children's door, in one brief shot Wednesday already has 2 dolls in her arms.
The Great Treasure Hunt - S2-E19
Revealing mistake: When Fester gives the anchor to Morticia, she drops it, and it bounces back up. When she lays it down, the wire used to achieve the gag is easily seen.
The Great Treasure Hunt - S2-E19
Visible crew/equipment: When Morticia bounces the anchor on the floor, the wire used to make it bounce is visible when she puts it down.
Happy Birthday, Grandma Frump - S2-E22
Continuity mistake: As Morticia and Gomez play with the train, there is only one train on the set. When Gomez blows it up at the bridge, there is a second train in the midst of it. This is a reuse of stock footage.
Visible crew/equipment: As Mr. Hinson and his aide get out of the car, the shadow of the boom mic is visible on the house.
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