When Thing hands Morticia the telephone, he is a left hand instead of his usual right.
When Fester lights Digby's cigar, it makes a large cloud of smoke. It then cuts to Fester and back to Digby, and the cloud is still in the same place.
In shots of the bear on fire, it still casts a shadow of an unharmed bear.
When Henson and Digby pull up to the Addams house, Henson can be seen talking in the car, but no sound is heard.