Continuity mistake: While Jaime and the High Sparrow are standing beside Myrcella's body in the Sept, in the overhead shot of Myrcella her right hand is placed over her left hand, but in other shots it's the opposite way. (00:18:30)
Continuity mistake: In one shot Sansa is writing a letter to Petyr Baelish, and is pressing a seal onto hot wax on the lower right corner. The next shot Sansa raises the letter, and the wax is gone. (00:39:45)
Other mistake: The faith militant attacks Gregor Clegane. Gregor chokes him. You will see that before the faith militant drops his weapon with his left hand, both of his hands are already holding Gregor's massive arm. (00:13:05)
Battle of the Bastards - S6-E9
Continuity mistake: When Jon Snow is all alone in the field drawing his sword to fight the incoming enemy cavalry, behind him we see an empty field. but seconds later as the enemy cavalry is near him they are met by Jon's own cavalry from behind. (00:37:30 - 00:38:20)
Battle of the Bastards - S6-E9
Revealing mistake: When Jon Snow jumps on the horse his steel sword wobbles back and forth revealing it's made of rubber.
Battle of the Bastards - S6-E9
Character mistake: When Theon and Yara are given an audience with Daenerys, Tyrion remarks to Theon that when they last saw each other at Winterfell, Theon was making jokes about Tyrion being a dwarf. The mockery was actually the other way around: Tyrion mocked Theon for being a glorified and subservient hostage of the Starks, as well as taking potshots at the foolish strategy of the Greyjoy rebellion.
Continuity mistake: When Sam hands the bureaucrat the letter from Jon Snow, in the shots facing the bureaucrat, the wax seal is on the left side of the envelope (when seen from Sam's perspective). In the shots facing Sam, the seal is on the right side of the envelope.
Answer: This is explained more in the book. Khal Drogo and his bloodriders do intend to help Viserys take the throne, however they do things in their own time. This is what causes Viserys's frustration. In the book, Illyrio Mopatis tells Viserys that he has already waited his entire life to claim The Iron Throne and that waiting a few more years isn't that big of a deal. The Dothraki are a nomadic tribe, which is largely why they have no interest in invading and sacking King's Landing. However, since Khal Drogo eventually grows to love Dany, her assassination attempt by the Westerosi compels him to seek revenge.
Phaneron ★