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: 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: 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: 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)
Suggested correction: It's not a hole, it's a arrow plumage. And camera's angle.