Roose Bolton claims that "He [Robb] ignored my advice at every turn". This is incorrect: in The Old Gods and the New (2012), Robb intended to return to the North and fight the ironborn invaders, but eventually accepted Roose's advice to send Ramsay instead.
When Tyrion talks with Cersei, the way he holds his wine glass changes repeatedly between shots.
Davos tells Stannis that his son Matthos taught him to read. Actually, Shireen taught Davos (Kissed by Fire (2013)).
Sam Tarly says the Wall is 500 miles long, while it is 300 miles long.
With the level of medicine and hygiene shown, there is no way Theon would survive a penectomy.
Tyrion's scar is inconsistent to his injury. The scar across his forehead is diagonal, the scar across his cheek is diagonal, but the scar across his nose is horizontal. The continuation of the sword wound should be consistent all across his face.
Jon is shot in the back and when he gets to the wall he's lying flat on his back. That would have pushed the arrows out through his chest and front of his leg.
Sam tells Bran "You're Jon's brother! The one who fell from the window!". Except Jaime and Cersei (and Catelyn, after Jaime revealed that to her), no one knows where Bran fell from. It was assumed he fell while climbing on the wall.
After Jon escapes from the wildings on horse, Ygritte catches up to him drinking from a pool of water. There are no indications that Jon stayed at the same location more than the time to get off his horse and drink, since he was aware he could be chased. When Ygritte approaches Jon, there is no horse in sight. Therefore, there is no way the encounter could have happened. In the book, Jon is injured by one arrow (possibly from Ygritte) in his thigh as he flees the wildings. They do not meet alone afterwards.