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I recall a couple of episodes where Andy threatened to spank Opie. It was never shown on screen that I know of, but there was at least one instance (when Opie had been playing with matches) where it was clear that the punishment had taken place between two scenes. There was also an episode where an incorrigible friend of Opie's threw a temper tantrum. Andy advised the boy's father that there was an old fashioned woodshed just out back. After the father dragged the screaming boy offscreen, Opie asked Andy if the kid was going to get a spanking. Andy asked Opie, don't you think he deserves it?
Back in the 50's and 60's, corporal punishment was a more acceptable form of discipline and at least threats and allusions to it were not uncommon on TV shows like Andy Griffith, Make Room For Daddy, Flipper, and others.