This episode was Peter Dinklage's submission in the Supporting Actor in a Drama Series category in the 2011 Emmy Awards- the first Emmy win and nomination in his career.
In the novel "A Storm of Swords", Jaime reveals to Tyrion the truth about Tysha: she was not a whore, but what she seemed to be - a crofter's daughter whom they encountered by chance and saved from rape. Tywin was angry when he found out that Tyrion had married a lowborn, and decided to teach him a sharp lesson: he commanded Jaime to falsely tell Tyrion that Tysha was a whore who had been paid to make him a man. Jaime felt bad about that, but did not dare to defy his father. When Tyrion learns the truth about Tysha after so many years, bearing in mind how she was gang-raped by the guards and by himself at Tywin's command, he furiously vows to exact revenge on Jaime, Cersei and their father. This twist of plot has been totally omitted from the show, reportedly due to lack of time.
In the book, Tyrion describes the Battle of the Green Fork from his point of view, only to find out that it was a mere diversion. There are some differences with the series: Gregor 'the Mountain' Clegane commands the troops; Tyrion wears an assortment of armor pieces from several suits, as his own custom-made suit is still at Casterly Rock, and he spears a horse for its unicorn helmet, the only thing that will fit on his head. After giving a battle speech, he fights in the vanguard, and miraculously manages to survive by successfully fighting several enemy soldiers himself. Afterwards, he tells his father that his plan to have him get killed in battle has failed. Tywin reveals that he had actually expected Tyrion and the hill tribesmen to run and retreat back to camp, hopefully luring the Stark army with them into a trap; Tyrion's unexpected bravery foiled this plan, and it was the Starks who retreated. The showrunners originally wanted to show the battle, but time and budget limitations during the first season forced them to cut the scene at the last moment, so this is the reason why Tyrion gets knocked out and the battle occurs off-screen. The success of season 1 dramatically increased the budget over the next seasons, allowing the team to depict on-screen battles in Blackwater (2012), The Watchers on the Wall (2014), Hardhome (2015) and Battle of the Bastards (2016).
It was revealed in an interview in March of 2018 with Sean Bean, that when Ned died, he whispered a small prayer to himself. In the beheading scene, he is mouthing some words, which up until then were a mystery.
Ned's beheading is slightly different from the book in a few notable ways. First, in the show Ned actually sees Arya in the crowd and sends Yoren to get her. Saving Arya from being captured ends up being his last living action. In the book, he does not know Arya is there, and Yoren sees her himself. As Yoren later tells Arya, he had not yet left King's Landing because Varys told him that Ned was to be given mercy, and would need a lift to the Wall. It is also notable that Arya and the reader do not actually witness the moment Ned is beheaded: the chapter is from Arya's perspective and in that moment she is being carried away by Yoren after she unsuccessfully tries to use Needle to cut her way to the front of the crowd.