Robert claims to kill a Tarly during the Battle of Summerhall. Actually, the Tarlys did not participate that battle; Robert first fought (and was defeated) the Tarlys in the Battle of Ashford.
Arya has her fighting lesson with wooden swords, but the sound is constantly of clashing metal.
When Daenerys and Drogo are lying in bed naked, imprints from a bra are clearly visible on her body.
When Eddard is walking into the throne room for the first time, the number of steps he visibly and audibly goes down do not match the actual amount of steps he descended (which can be seen when the camera angle changes to a front view of him).
All characters at the Wall wear elaborate furs. However, all northern people know that it's the head you should protect most, but no one is wearing any kind of hats. Also, there are very few beards - the best face protection against strong winds.
Joffrey refers to Kevan as his uncle. Actually, Kevan is Joffrey's great-uncle.