Continuity mistake: When Tyrion wakes up inside the skycell you can see two skylights in the ceiling of the cell through which the sunlight passes. However, when we get a long shot of the skycells, you can see there's no way for the light to pass through them, as there are no "holes" on the floor of the cells above Tyrion's. (00:13:45)
Continuity mistake: When Ser Vardis has cornered Bron right at the edge of the moon door the position of Bron's body changes between shots. When the shot is taken from inside the moondoor, Bron's body leans backwards, over the moondoor. But when the shot is taken from behind the throne Bron is leaning forward.
Continuity mistake: When the guard is hitting Tyrion in the sky cell, Tyrion has his arms outstretched in one shot and against the wall in the next. (00:14:00)
Continuity mistake: When Bran is taken from his horse in the woods, there are 3 wildlings that attack. The first Rob cuts his throat, the second, Rob is holding the female wildling by the hair, he then spears and kills the third with his sword and the very next frame the 3rd wildling is then holding a knife to Bran's throat, unharmed. (00:11:15)
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 ★