People seem to be criticizing a lot of the characterization in this episode, especially that of the Doctor.
It’s important to remember that Twelve is a new Doctor. As with every regeneration, we tend to figure out the new facets and characteristics of a new Doctor along with the companions. Admittedly, Twelve is probably the most markedly different Doctor since New Who started up.
We’ve seen that Twelve is brasher and harsher than ever, certainly a strong difference from the gentle child-like qualities we’ve seen with Eleven and even Ten. We’ve seen plenty of scenes with a darker Doctor (Oncoming Storm has been present throughout the seasons), but this is no longer a childlike, goofy Doctor who occasionally switches to an ancient, unknowable being when pushed to the limit. Twelve himself is stranger and more capricious than ever, and Kill The Moon reflects that.
Clara called him out on everything he probably should have been called out for. Twelve feels very, very different from Nine, Ten, and Eleven because he’s changed fundamentally from the Doctor that we’re used to seeing. Was it out of character that Twelve said Courtney was nothing special? Perhaps. But it’s also possible that the Doctor has become something entirely new. The Time War must be viewed in an entirely different light now, and clearly the Doctor has changed significantly.
Capaldi’s Doctor is the anti-hero. He lacks the endearing silliness that characterized his previous incarnations. Something has changed, and Clara is coming to terms with the fact that she’s not sure if she likes who the Doctor is anymore.