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.
The New Neighbors Meet the Addams Family - S1-E9
Revealing mistake: As the Petersons look at the square of carpeting coming up, the wire pulling the door up is visible.
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.
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