Ned asks some more questions and establishes that the baddies weren't waving a giant banner, which would have been awfully obliging of them. However, one of them was extremely tall and cut the blacksmith in two. He also decapitated a horse, so it's obviously Gregor "The Mountain" Clegane. Littlefinger leans back and reminds Ned that the Mountain is sometimes called "Tywin Lannister's mad dog." He asks, "Can you think of any reason the Lannisters might have for being angry with your wife?" Ned glares at him and decides it's time to make a pronouncement. He calls forward a lord to assemble a hundred men and ride to Ser Gregor's keep. The Mountain is stripped of his title (by which he means "Ser," not "The Mountain," presumably. Because "The Mountain" isn't a name you can strip from someone) and sentenced to death.
Pycelle thinks this is hasty, what with the actual king being out of town. Ned also wants a raven sent to Casterly Rock to notify Tywin Lannister that he must come to King's Landing and answer for the Mountain's crimes. Or else he'll be branded a traitor. So I guess that truce between the Starks and the Lannisters isn't going to come off exactly as Robert was hoping.
That's the end of court, and Littlefinger has a brief confab with Ned. He thinks Ned's being both bold and admirable, but possibly not wise. Ah! I learned this from Yes, Minister: if you want a politician not to do something, you tell him he's being very brave. But Ned's not a politician. Littlefinger tells him, "Gold wins wars. Not soldiers." Ned points out that Robert is king, not Tywin. So that means he has confidence in Robert's ways of doing things? Because I'm not sure "The Seven Management Secrets of Robert Baratheon" would contain much except drinkin', whorin', and killin'. And that leaves you missing four management secrets.
The Moon Door is staying open for Tyrion's trial. And that trial is taking the form of him standing there and watching Bronn fight against Lysa's handpicked knight. Robyn initiates the festivities by screaming, "FIIIIIIIIGHT!" The knight is armored and has a helmet and a shield. Bronn is dressed much more lightly. The knight chases after Bronn, who backs away, hopping over railings and knocking things over. Onlookers are getting impatient with this plan. Especially when Bronn throws an onlooker in the way of the knight. At one point, Bronn is backed up against the Moon Door, but he escapes for another trip around the room. Lysa tells the knight to quit screwing around and finish Bronn off. The knight rolls his eyes a tiny bit and lowers the visor of his helmet. He goes in for the kill, but Bronn slices him up the torso. The knight gets to his feet and charges, but Bronn steps aside and trips him. He kicks away that shield and grabs the knight's hand. He takes a moment to look around at the assembled masses, then lifts his sword. He goes for another dramatic pause, then carefully inserts it into the knight's neck. There is lot of blood. And then Bronn kicks the knight's body into the hole and he falls into the sky. So long, knight!