Video Other mistake: As the surviving characters discuss the fate of Westeros, 2 plastic water bottles can be seen tucked behind the chairs they're sitting on.
Video The Last Of The Starks - S8-E4
Other mistake: During the scene in the banquet hall, as Tormund says "most people get bloody murdered, they stay that way", look at Daenerys in the background - a disposable coffee cup is on the table in front of her. This brown cup with a white plastic lid is nothing remotely like the style of cups they're all drinking from in the scene. HBO acknowledged the slip up and digitally edited it out on streaming services, reruns and future DVD releases.
Video Trivia: One of the severed heads on a spike is that of former president George W. Bush. Before shooting the scene, George RR Martin asked writers and producers David Benioff and D.B.Weis to have a cast of their 3 heads to be put on the spikes, but for budget reasons they opted to get a box from HBO's warehouse with used severed heads. They noted that one was Bush's, but they put a wig on it and got away with nobody noticing. In the Blu-Ray commentary the producers revealed the story, and got a lot of criticism from the right.
Answer: As Hand of the King, Tywin is the second most authoritative person in Westeros behind only the king. The Hand's duties include sitting on The Iron Throne and dispensing order, justice and judgment, similar to what Ned Stark did in the Season 1 episode "A Golden Crown" while then-king Robert Baratheon was out hunting. It's also worth pointing out that Tywin's enormous wealth makes him the de facto most powerful person in Westeros, which he demonstrates in the Season 3 episode "Mhysa" when he sends King Joffrey to bed without his supper and remarks to Tyrion "You're a fool if you believe he's the most powerful man in Westeros. Do you really think the crown gives you power?"
Phaneron