Charles has not done anything, as far as I can recall, that casts any doubts on his ability to be a good Monarch. Certainly nothing that the public could lay down as a water-holding concern, in my opinion.
HMtQ survived the aftermath of Diana's death and the mass hysteria that went with it - which has to count as the only really large blip on the royal radar during her reign. If she can survive that craziness, Charles can survive what remains of the aftermath of a broken marriage and an adulterous affair.
I think most people, in the fullness of time, have come around to accepting that Charles, while not strictly "the good guy" is, by the same token, not "the bad guy" vis a vis his relationship with Diana.
One of the ways in which public opinion is formed, in this modern, post-war age, is based upon the perception of a person's character as evidenced by their family relationships. Most people seem to feel that Charles was a good father and this translates, just under the consciousness, into his being a good Monarch. The role, itself, is very paternal/maternal by its very nature.
I do know that my opinion of him, while always respectful and moderately high, really peaked when I saw him in a few videos with William and Harry. These are people that genuinely love and care about one another. It made me have a new sort of respect for him. In my world, talking to plants is part of the daily program and having earned the genuine love and trust of my children is a bit, a big bit, of the life goal.
Further, I was very much against Camilla in the beginning. But as time goes on and I see Charles' face more relaxed and his demeanor more happy, as I hear nothing but positive reports about her activities and duties, as I come to more fully understand the Diana years, I have built a respect for her. When they are together there is a great kinship between them and I am pleased that he found someone, at long last, who can be a helpmate for him, a true partner in what has to be one of the most demanding and daunting duties in existence. I am happy for them and in that he was always going to be the King, no matter the Queen Consort, I would rather he be happy with his Consort than bound by a lifelong duty in a situation that was unhappy.
I mean, he's going to die on the throne, being my King. The least, it seems to me, that I can offer back, is support for the partner he has chosen to help him meet his duty to me. It came grudgingly, though, I do admit.