To begin, not all of the examples I will share are exactly the sort of controversies you may be referring to, but were groundbreaking and certainly controversial for the networks involved.

First, although Lucille Ball and Desi Arnaz were already celebrities, the adaption of their popular radio show to TV in 1951 almost didn't happen as network executives thought the depiction of an on-screen interracial couple would not be accepted by the general public. It was only after successful ratings of test audiences that it was given the green light.

"I Love Lucy" later had executives wondering how they would handle the fact that Lucile Ball was pregnant, and such a topic would be too controversial. Again, the shows production continued and made episodes based on her pregnancy and birth, but not without limitations (see one source at bottom of comment).

Another topic that comes to mind was the first tv on-screen depiction of a couple laying in the same bed, which, technically, was done in the show "Mary Kay and Johnny."

I am sorry for the lack of better sources, I have many but am away from home at the moment. Early tv is topic of interest for me so if you or the mods would like me to elaborate, edit or have further questions or examples, let me know and I will gladly do so later this evening.

http://www.snopes.com/radiotv/tv/marykay.asp

http://www.avclub.com/article/more-than-60-years-ago-a-pregnant-lucille-ball-cou-100629

Again, I am sorry for the sources as I am on the fly. This is not how I want my first askhistorians response to be, but it's what I can do at the moment.

Television before 1960 was such a new technology that you would be hard pressed to see anything controversial at all because everybody was still trying to figure out simply how to do anything at all with the medium. What programming did happen was usually live, and largely experimental with just about everything, including common concepts now well established like commercial breaks, half-hour or hour long programs, and even how to address the audience in the first place. Those who did participate in television programming either had a radio background or came from both the film and stage theater... or were completely new to any sort of acting or performance experience.

Of the radio shows that were controversial before 1960, perhaps the most famous that I can think of was the War of the Worlds broadcast done by Orson Wells in 1938. It was definitely as edgy and controversial as anything done with South Park.... likely even more so than anything done since at least in terms of audience impact.

There certainly were other controversial radio dramas, including entire series that were produced in the 1920's and 1930's, although something to keep in mind is that the production costs for a national broadcast were sufficient that it probably kept the most controversial kinds of productions from being done simply because nobody was willing to pay for such productions if they got too edgy. One of the things that makes it possible for people to push boundaries today is the plethora of available outlets for people wanting to publish such content. That is definitely different than was the case in the past.

Orson Welle's radio broadcast of the War of the Worlds in 1938 was controversial because some listeners thought there was a real alien invasion going on. There was a disclaimer at the beginning of the broadcast, but not all listeners tuned in from the very beginning. In spite of sensationalist claims the number duped was quite small but it can be seen as an early example of "pushing the envelope". There's plenty of sources, but you should read Frank Brady's biography as a good starting point.

Ugh my mobile device ate my response twice now. So here's the basics about flying saucer programs pre 1960:

• Frank Edwards did many radio programs about flying saucers in the late 40s and early 50s.

• Long John Nebel's late night show frequently discussed UFOs in the 50s. Wendy Connors' Faded Disc Archive is on archive.org and has multiple Nebel shows

• The most controversial program was Donald Keyhoe's live but scripted debate with representatives of the USAF in 1958 on the Armstrong Circle Theater. Keyhoe announced he was going off-script and his mic was cut before he could say a Congressional committee was seriously investigating UFOs. This was clearly censorship, and many people were upset by it. The tape doesn't exist anymore to my knowledge. Keyhoe discussed the event with Mike Wallace, video here.

And I've read that astronomer and USAF advisor J Allen Hynek appeared on a tv show also with Aldous Huxley around 1952ish. Sadly that also seems to be lost in time.

Now I don't know if UFOs would have offended granny. But it was a controversial subject back then, even before the full culture of conspiracy had grown up around it.