So far so conventional. Series writer Talbot Rothwell actually wrote the lion's share of the Carry On films so the tits-and-bums approach isn't that much of a surprise. The redemptive reading comes from the lead actors:
Frankie Howerd and Max Adrian were gay, you see, and this would not have been unknown to Rothwell. Neither of them may have been out in the modern sense but neither were closeted in their professional lives. Adrian himself was out to the acting world at least as early as 1965 (when his orientation caused some friction on the set of the Doctor Who story The Myth Makers, in which he was excellent, by the way).
So what we have is a series anchored by two homosexual men (at least in the first season) acting out the worst stereotypes of heterosexual men for laughs. They are also shown to fail constantly, which is the point of farce: the narrative is both on their side by presenting them as the heroes of the piece and against them because it is forever making them suffer. Add to this the fact that Nausius can easily be read as closet gay (“Yes, they had them in those days, too,” Howerd confides to camera before reading the first of Nausius' many awful odes) or in denial: constantly pursuing woman but with no idea what to do with them on the rare occasions they don't tell him to sod off.
The thing is that Nausius is actually quite a nice, sensitive person. This being a farce that means he is almost always cast as a foil either to his father or to Lurcio in some scheme or other (including the compulsory crossdressing subplot when the two older men need to find a vestal virgin in a hurry) but of all the characters in the show he is the only one who ever acts heroically. There are a couple of episodes that have him disapprove of slavery and one where he even frees two slaves (woman, naturally, that he has “fallen in love with”). He's also very open about his feelings when the rest of his family are constantly lying to and cheating on each other.