When Thing hands Morticia the telephone, he is a left hand instead of his usual right.
Kitty-cat supposedly was served broiled elephant hooves.
Elephants don't have hooves, they have toes.
When Kitty-Cat is shown in the tunnel, the background moves slightly, indicating a projected image. The cat also looks very different from Kitty-Cat's usual appearance.
When Gomez and Morticia play their cellos, their fingering, particularly Morticia's, does not match their playing.
The "African crocodiles" scene is stock footage of American alligators.