Continuity mistake: When Bran is asking about where his mother has gone he is playing with a lure. Between instant cuts the position of the lure in his hand is constantly changing. (00:15:20)
Continuity mistake: After the attack on Catelyn we see Bran Luwin and Theon talking while Theon is practising archery, the arrows in the board are constantly changing position and appearing and disappearing with no time to do so. (00:13:50)
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 ★