Back at King's Landing, Joffrey has his first court appearance as king, which might stand as the textbook definition of paranoid.
Joffrey demands a whole lot of people come to swear fealty to him. (Actually, that's probably not that crazy: it's just what they did back then.) He makes Janos Slynt a lord (payment for turning on Eddard Stark).
Joffrey also relieves Barristan Selmy of his role in the Kingsguard. This makes Barristan very angry and he says something about how Stannis may soon be the king. Hmm.
Instead, Sandor Clegane is made one of the Kingsguard, though Sandor isn't a knight. (Check out Sandor's "Character Analysis" for some discussion as to why.)
Sansa asks for mercy for her father; and Joffrey and Cersei say that they will show Eddard mercy if he confesses to his crime.