Don’t ask, don’t tell. 
Vivian Vance’s character on The Lucy Show was a divorcee, but that was seldom mentioned aside from the odd alimony joke. Her ex never showed up onscreen.
IIRC there was an episode where a nude painting of her surfaced (she didn’t actually pose nude; the artist used his imagination). Naturally the painting itself was never shown.
When Paladin had a woman in his room, he’d get interrupted after the fun, not before. Though I must admit in the very first show he is introduced as he goes down the stairs to the lobby along with a woman who has a quite satisfied smile.
And the would be able to mention gas in the TV version of “Judgement at Nuremberg.”
Jack would be allowed to living an apartment with two girls regardless of his sexual preference.
Even if the building owner was some tight-assed fundy?
Match Game wouldn’t have been as fun if there were no rules to bend.
Oh, she’d have called Tony “Master.” 
But she would not have lived in a bottle … she would have had a nice, roomy cage.
Among other things …
The A-Team would be a bloodbath.
And Petticoat Junction would’ve been my favourite show.
Mary Kay and Johnny, considered to be the first-ever sitcom, showed a married couple sharing a bed way back in 1947. There was no regulation against it, not even a Hays Office type production code. Sponsors owned the programs back then, and sponsors wanted to avoid anything that even smelled like controversy.
The show that actually broke the twin bed barrier was, believe it or not, Ozzie and Harriet. The home the show was set in was pretty much an exact duplicate of their real-life house, and they insisted that since they were sleeping in one bed IRL, there was no reason not to on TV. They won the argument because they owned the show.
TV censorship was FANTASTICALLY restrictive back in the 50s and 60s – it was basically all children’s programming. Newton Minnow’s “vast wasteland” indeed. Entertaining without offending generally tends to produce boring entertainment.
Imagine what kind of hijinks The Partridge Family would have gotten up to after their concerts without censorship.
No, wait, don’t do that. I don’t want to be responsible for any horribleness you can’t unimagine.
There’d have been more scope for innuendo jokes based on kids innocently misinterpreting things:
“Daddy, what’s bondage?”
<beat.>
(poker face) “How do you mean?”
“It says in the Bible ‘I am the LORD thy God, which have brought thee out of the land of Egypt, out of the house of bondage.’”
“It’s another word for slavery”.
“Oh; ok!”
(dad facepalms with relief)
OR
“Mom says she likes Howard’s Johnson”
“That’s Howard Johnson’s”!
Keith would never have said “Of course I like girls, but only one at a time!”
Come to think of it, neither would I. :o
I disagree if you are referring to anything more than sitcoms. Until All in the Family hit the airwaves, sitcoms were pretty bland. Shows like Peyton Place could get pretty seamy, though, and the drama anthology shows aired some pretty hard hitting stuff.
There would be nonstop sex sounds coming from Fonzie’s room above the garage.
I recall an episode of “Happy Days” in which Richie asked Fonzie what he does with the girls in his room. Whatever explanations he gave made me wonder why Richie was so interested.
For a guy with girls constantly hanging all over him, Fonzie was strangely non-sexual.