Most of the jokes are aimed at the fussy stuffiness of the Royal Family. And while at first it seems mean spirited as if mocking the Royals, the story is not one sided. While at first it is easy to just say, oh the royals got it all wrong, as the movie progresses you see that they are simply behaving in a way that tradition has dictated they behave. As the Queen tells Blair at one point, “I am behaving with good manners and quiet restraint. Two attributes that the world has long admired us for.”
By the movie's end, you can not help but have respect, even if you feel that she's outdated and anachronistic, for the Queen. Of all the Royals, it is Charles who comes off looking the worst. He is portrayed as weak, desperate for the public's support and even worried that he might be shot in the aftermath of Diana's death.
Both Sheen as Blair and Mirren as the Queen deserve credit for their performances. Neither of them do impersonations so much as they simply embody their respective characters. They look just enough like their subjects, but it is the performances that bring them to life.