I think sometimes we can analyze too much and focus on political correctness and not offending anyone ever, to the point that all the funny is sucked out of this show 😐
Not disagreeing. I love The Office (U.S.), for example, and despite how popular (and lucrative) it remains, it couldn't be made today. All in the Family -- hell, all of Norman Lear's groundbreaking sitcoms that explored and confronted social issues through the genre of comedy would be viewed today through a binary, not nuanced, lens.
My point about Caroline is about dehumanizing her and, as @starryjonquil accurately replied, stigmatizing people with mental illness. That's a distinct issue from political correctness.
To use The Office as my example again, the show is written so that the audience knows what Michael Scott is saying (and doing) is wrong. The other characters affirm this fact. Yet his ridiculousness is still hilarious, and it doesn't make me think, "Hmm, X-culture or X-people are what Michael thinks they are." Or that how he approaches certain subjects and people are correct.
Archie Bunker from All in the Family is the prototype for this kind of character. And Meathead is his foil.
