Continuity mistake: This is when the family is watching Bran practicing archery. The round target on the left has a large hole on the bottom right side, presumably from a previous arrow. This hole moves around throughout the scene, most noticeably in the shot after Arya shoots an arrow right into the middle of the target. (00:10:40)
Continuity mistake: When we see the dead deer at the start there are maggotts all over the face of the deer. Between camera angles, the position of the maggots differ drastically. (00:15:00)
Continuity mistake: Ser Jorah has just given Daenerys 3 books as her wedding present. As she takes them, their spines are pointing towards her right side. Cut to the next shot, as Jorah informs her that he served her father, the spines are now pointing towards her left side. (00:50:45)
Continuity mistake: At Daenerys' wedding we see a man get sliced across his midriff and lean backwards with his mouth open. Camera does an instant cut and now he is slouched forwards. (00:52:00)
Continuity mistake: Khal Drogo has just lifted Daenerys onto her horse after their wedding celebration. Her hair is behind both shoulders. In the immediate next shot, her hair has now moved in front. (00:55:00)
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.
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.
Suggested correction: It's not a hole, it's a arrow plumage. And camera's angle.