At this point, Tyrion comes in to condescend at Joffrey, be nice to Sansa and call the Hound ugly. He ever-so-subtly reminds Joffrey (and the assembled throngs) that he's just been in a giant battle while Joffrey sat on his kickable butt. He also tells Sansa he's sorry for her loss which prompts Joffrey to be outraged that anyone would be sad that their father died, since he was a traitor. Sansa recites an obviously well-rehearsed line about how all her relatives are traitors. Tyrion strolls off to do "work" without telling Joffrey why he's there. Tyrion is followed by an awful lot of goons. He appears to have brought his own army into King's Landing. Probably a good idea, right? At times like these, you want an army with you no matter where you go. And he was sent by Tywin to try to rein in Joffrey, which is definitely something you'll want some muscle for.
Elsewhere in King's Landing, Cersei is running the Small Council. And she's received a message bird! I give that sentence an exclamation point because I personally have never received a message bird. Or a telegram, now that I think of it. In fact, it's been awhile since I've gotten a regular letter. I seem to have gotten off the subject of the message bird, which is that there are problems in the city. She wants peasants left out in the fields where there's a war going on, rather than allowing them into the safety of the castle. Tyrion strolls in, whistling. He does a lot of strolling in this episode. He seems pretty pleased with himself. Cersei wants to know why he's there, and he cheerfully tells her about all the wall-pissing and hill-people-hiring he did in the last book. Um, "season." She reminds him that this is the Small Council, which is only for very important people like her and Varys. Tyrion informs her that "father" has made him Hand of the King in his stead.
Cersei throws the tertiary characters out and shouts at Tyrion for a bit. He denies having done anything wily to get the job and blames her for not stopping Joffrey from killing Ned and starting a war. They agree that Joffrey is king and that Tyrion is just here to advise him. And then Tyrion tells her that they might get Jaime back if nothing else stupid happens. She admits that they lost Arya so they only have one Stark child left to barter with. Tyrion blames her for not keeping Joffrey in line: "We had three Starks to trade. You chopped one's head off and let another escape." Then he twists the knife by calling her "the disappointing child." Hey, at least she didn't get captured like Jaime. That guy's really letting the side down.