As a kid, I always realized when a sitcom was "taped before a live studio audience" or "filmed before a live studio audience". And it's funny that the fact that one of the cast members told me at the end had nothing to do with it. Funny, I've never been a technical person, but I always bugged my family and friends with this fascinating observation. The reply was usually, "I don't really know but the show is funny (or lousy)."
In the fifties, Desi Arnaz created the three camera studio audience setup with "I Love Lucy". Most comedies were broadcast live across the nation (kinescope), and were never saved in any way for posterity. In the mid-fifties, sitcoms started using the recorded laughtrack in lieu of a live audience. This allowed for more intimate closeups and outdoor shooting (you know, for when the Beav confronts the bully). In the sixties, most sitcoms used laughtracks due to the special effects (Bewitched, Jeannie, Beverly Hillbillies....well actually the special effect on the Beverly Hillbillies was that it was a top-rated series for eight or so years). Dick Van Dyke and Lucy were the few exceptions during this time.
Mary Tyler Moore's sitcom premiered in fall of 1970 with the three camera audience setup. Then four months later, Norman Lear brought All in the Family to the forefront of the American scene. Lear based many of his landmark sitcoms on British series and like those series he realized the cost savings in shooting on videotape. Videotape is cheaper than film. He even eliminated establishment setting tags (like the musical cue with the apartment/office building zooming in). So his made the shows pretty cheap to film.
To complete the history, M*A*S*H was one of the few seventies sitcoms to use a laughtrack (and that was controversial). In the 80's most sitcoms decided to go cheap and they looked cheap on video. Newhart's second series started on video and for reasons I will explain later, switched to film for the next seven years. In nineties, almost all sitcoms (ala Friends and Seinfeld) had that filmed studio audience. This became the standard "look". Otherwise there was no audience at all (The Office, 30 Rock, Arrested Development). I believe a lot of the "filmed before a live audience" sitcoms these days are actually done on video that mimics film. If you close one eye and stand on your head you can see it during any unfunny scene.
For some reason (or many obvious reasons), filmed sitcoms seem so much more realistic. With taped sitcoms, it was like being in the audience, a stage play almost. You could hear the audience coughing sometimes. This worked with the Norman Lear comedies because they were a form unto themselves. The acting and writing were superb at first. Then as the seventies moved into the eighties, poorly written sitcoms with stagey acting were taped. This just made filmed shows look so much better.
At first, it was shocking. Soap operas and variety shows were taped. Not sitcoms. They were bright, heavily lit. The sets looked like sets. When four people sat around the dinner table hey left a gap for the audience to look in (like a play). I have no idea why this "table" thing was different for film--the medium shouldn't have anything to do with staging. There were more up close close-ups. The audience had to applaud when the actors entered. Actually, Garry Marshall did this on his filmed sitcoms...enter Fonzie or Laverne.
Speaking of Happy Days, remember the first episode filmed in front of an audience? Fonzie dated the stripper? Still the funniest episode.
Did you know the first season of The Odd Couple was filmed with a laughtrack and no audience. It moved to a soundstage in 1971 during the second season. That set would end up as Laverne and Shirley's apartment. It is now the condo from Two and a Half Men. (It's a good thing Laverne and Shirley moved to Hollywood in 1980).
Did you remember that the first season of "Newhart" (the innkeeper in Vermont version) was videotaped? The remaining seven seasons were filmed. Bob just had to be filmed. It seemed that the original Bob Newhart Show always hued brown earth tone colors amidst a sea of checkered polyester. Here is rare videotaped Bob:
And did you know that even though Barney Miller was taped during its entire run only the first two seasons had an audience. After that, the producers would screen the finished episode to a live audience and capture the reactions. All in the Family did this as well during the Stephanie year and all the Archie Bunker Place episodes. This allowed more improvisation on the set I suppose.
Speaking of Barney Miller, that was was the best looked videotaped sitcom. The producers used a filter to give it a grimy, New York feel. Very effective.