When Talisa amputates the soldier's foot, she claims it is because the 'rot' has set in. However, the battle had only happened the night before, not leaving enough time for putrefaction.
When Tywin rides into Harrenhal, his sash switches from one side to another.
Melisandre claims that Stannis was "born amidst salt and smoke." Dragonstone, a volcanic island, can be considered as a place of salt and smoke, but Stannis was born on Storm's End.
When the door opens to Qarth to let the Dothraki in, there is a view of the town and a river in the distance. When it reverts to the long shot, there is a closed gate immediately after the main entrance, and the river is no longer visible.
When Arya adds Polliver and the Mountain to her prayers, her lip movements don't match when she says "the Mountain."
Melisandre refers to Davos as "Davos Seawood." His family name is Seaworth.