RE: The Cosby Show and characterization-Cosby wasn't the butt of the joke every week in the way Archie was, and I wouldn't say that was a huge part of the show. If there was anyone who was most often the butt of the joke, it was probably Denise or Vanessa-Theo too for a good chunk of the show, but by the end he grew out of it. There were, however, many instances Claire was treated as the wiser, more sensible parent and Cliff thus would occasionally become the goofy one.
Not in the sense that he was a bumbler-and he got the key "lay down the law" scene to set Theo straight in the show's first episode, something that still would have fit his character in the last episode-but mostly because Cosby liked to riff and go off on silly tangents whenever he felt like it. Unlike some other comedians that headlined sitcoms, he enjoyed hamming it up, which sometimes, but not always, resulted in him becoming the butt of the joke.
Not in a way that's really comparable to Darrin, Archie, or some of the other examples, though.