Some shows I associate with either one of my parents, but Barney Miller is a show where I know both my parents equally enjoyed it and watched together. Dad loved Hal Linden going back to his days as a Broadway star and Mom really helped me appreciate the subtleties in humor and the more serious moments.
I think this is the first comedy I watched where I felt sad for a character. It was the episode where Chano, played by Gregory Sierra had killed a man, and how he dealt with the aftermath. They showed him breaking down crying in his apartment. It was really rough to watch. I would have been 11 or 12 at the time. I also remember in that same episode there was a tremendous delayed and then sustained laugh when he comes back from a movie and someone asks what he saw and he says, "Dirty Harry." (I think mom had to explain that one to me.)
The first show where I remember knowing that a character had left the show and been replaced with another one. (Gregory Sierra left and we got Dietrich, played by Steve Landesberg).
Dietrich was one of the first characters I really related to. He was so smart and the other characters (especially Harris) seemed to resent him for it, and that was definitely how I perceived myself at the time. The character was basically Landesberg's stand-up persona transplanted to the sit-com settiing. My dad loved him too, from seeing him on the Tonight show. He was the original deadpan snarker before the word "snark" was in any kind of popular usage, and the way he'd get a line in there, almost under the radar has always been an inspiration in my own approach to humor.
I wasn't shipping slash then, but I think in retrospect, the Harris/Dietrich relationship was damn close to "foe-yay."
Probably also the first show I watched where I was aware of an actor having died, when Jack Soo passed on and they did a tribute/clip episode about Yemana.
One of the great "work-place" sitcoms, even more purely than Mary Tyler Moore show. There were SOME scenes outside the precinct, but not many.
One of the greatest New York shows of all time. Even if it was shot in a studio, it still FELT like NY. Look at those credits, see the Towers and feel the NY of the 70's.