In the show, you couldn't see what was dialed. He just kind spun the dial a few times, without letting it return properly. They didn't want to waste air time while properly dialing a number, slows the pace down too much. Indeed, today on TV you'll see people just shove their hand against a Touch Tone pad rather than properly press buttons one at time to make a call.
Perhaps the show originated out of New York City, not Hollywood. I think the writers (who later were famous comedians and producers themselves) were New Yorkers, or at least New York oriented.
A separate number for Long Distance instead of plain zero was common in many cities. Long Distance switchboards were differently equipped than dial-0 boards (calugraphs*, long distance trunks, number verification panel, etc.), although many places used one operator.
I wonder when 211-long distance was discontinued. I don't remember it in my phone book, even before we got DDD (we just dialed 0). Dialing
211 got the regular operator.*Not to be confused with "calutrons" which was a suped-up cyclotron used to refine unranium at Oak Ridge Tenn.