Diana Rigg's surprised exclamation towards Gwendoline Christie's height, when the latter approached her table, was quite genuine. Rigg was aware that Gwendolyn was taller than most women, but was unprepared for just how tall. The producers kept it since it fit in so well with her character.
In the book, the conversation between Tywin and Jaime soon turns into a fiery exchange of words: Jaime insists on staying at the Kingsguard despite his maiming, and yells furiously at his father that he does not want to marry Margaery, and does not want Casterly Rock. Tywin responds harshly "You are not my son". This is their last conversation.
While reading the White Book of the Kingsguard, Joffrey mentions Ser Duncan the Tall, the main character of the "Dunk and Egg" trilogy by George R.R. Martin. It is the second time Duncan is mentioned in the show, following Game of Thrones: Lord Snow (2011).
The Valyrian steel sword Ice belongs to House Stark. It was used by Eddard in Game of Thrones: Winter Is Coming (2011) to behead a Night's Watch deserter, and in Game of Thrones: Baelor (2011) by Ilyn Payne to behead Eddard. In this episode, Tywin hires one of three people in the world that can work Valyrian steel to make two swords, one for Jaime and one for Joffrey as a wedding gift.
The creators of the show, David Benioff and D.B. Weiss, both directed this episode even though it was only Weiss that was credited for it eventually. Limitations of the Director's Guild restricted them from having both their names credited for the episode, so they agreed that Weiss will be the sole credited director of this episode, after Benioff was solely credited for the episode "Walk of Punishment" from the third season, which they also directed together.
Although Valyrian steel and the Valyrian language are frequently mentioned on the show, the Valyrian civilization, its location and fate are hardly ever discussed in detail. Valyria was a grand capital of the Valyrian Freehold, which covered most of the continent of Essos. Four hundred years before the start of the show, the city was almost completely destroyed during the Doom of Valyria, a series of massive volcanic eruptions and earthquakes. The disaster also seriously decimated the dragon population on the continent, and the ensuing collapse of the Valyrian realm indirectly caused the surviving Targaryen family (and their dragons) to invade Westeros almost a century later. This episode is the first to explicitly mention the Doom, as well as acknowledge the fact that the craft of manufacturing Valyrian steel was lost during the cataclysm (although a few blacksmiths can reforge existing Valyrian steel). The Doom of Valyria is actually the very first thing seen in the show's opening credits, depicted on one of the rotating rings as a city in flames on the slopes of an erupting volcano, next to a dragon.
The trivia item below may give away important plot points.
In the books, the brawl at the inn occurs in much later point of the story than in the show. It is significantly different than in the show: the people whom Arya and the Hound encounter are Polliver, the Tickler and a squire of House Sarsfield; in the ensuing brawl, the Hound manages to kill Polliver, but is severely injured; Arya kills the squire and the Tickler; soon after Arya and the Hound leave, he collapses and Arya abandons him.