Visible crew/equipment: Whenever Thing comes out of his little places you can see a wire that is used to open up the little hiding place.
The Addams Family Goes to School - S1-E1
Visible crew/equipment: When the phone rings and Thing hands it over to Morticia, the camera zooms out and you can the actor playing Thing quickly hide behind the couch. (00:24:15)
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
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.
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.
Morticia and the Psychiatrist - S1-E2
Visible crew/equipment: When Uncle Fester climbs down the tree (after observing Pugsley interact with the shrink, a shadow of the moving dolly mic is visible as it moves backward. (00:22:35)
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.
Other mistake: As Kitty comes down the stairs, Hilliard screams, and Kitty goes back up. It's obvious the film was run backwards.
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.
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.
Other mistake: As Fester goes to shoot Gomez, his aim strays upward to about a 45 to 50° angle. Not enough to shoot the support chain on the light that is directly above him, and hits him on the head.
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 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.
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