A Knight of the Seven Kingdoms - S8-E2
Continuity mistake: During the battle strategy meeting around the table, Sansa wears the long silver chain and circle neckwear, and the long chain changes the way it is placed through the circle. Sansa's chain is put through the circle in a way that's over and under in most shots, but when Jon explains that if the dragons are in the field they won't be able to protect Bran, the long chain is put through the circle the opposite way, under and over. (00:30:05)
A Knight of the Seven Kingdoms - S8-E2
Continuity mistake: When Gendry gives Arya the dragonglass weapon that he made for her, in the following shots Gendry's leather cloak straps switch between being crossed with his left strap over the right strap, or his right strap over the left strap. (00:43:00)
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 ★