Continuity mistake: When Ned executes the deserter, the wide leather straps of Ned's cloak are crisscrossed with his left over his right. But when Ned walks over to Bran, the straps are now crisscrossed the opposite way. Not due to flipped shots.
Continuity mistake: When King Robert arrives at Winterfell, the wide leather straps of his cloak are crisscrossed with his left over his right, but when Robert and Ned walk inside the crypts, Robert's straps are crisscrossed the opposite way, with his right over his left. The shots are not flipped.
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)
Character mistake: Davos advises Grey Worm to claim land in the Reach and start his own house. Since Grey Worm is a eunuch, he cannot start his own house, as he cannot father children to pass his name and lands onto.
Other mistake: When Ned is about to behead the Night's Watch deserter, the deserter whispers, "Forgive me, Lord..." No major religion in Westeros refers to their deity or deities as 'Lord'.
Suggested correction: But Ned is a Lord. His Lord even. He asks Ned for forgiveness.
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.