Jon's beard changes in the last shot of the scene where he talks to Jaime.
In Winter Is Coming (2011), Jon and Robb are clean-shaven. At the beginning of this episode, which starts at the point the previous episode ended, they have completely regrown their hair and stubble.
Tyrion and Jon say that Tywin was the Mad King's Hand till Jaime killed him. This is incorrect: Tywin resigned from his office as the King's Hand long before Aerys's death, and four men officiated in that office after Tywin: Owen Merryweather, Jon Connington, Qarlton Chelsted and Rossart.
At the fork of the Kingsroad, Eddard is heading south to serve at King's Landing, and Jon is heading north to serve at the Night's Watch. But after they say goodbye, Eddard takes the north road, and Jon goes south.
In the first scene of the episode where Jorah is telling Daenerys about the Dothraki's beliefs, the clips of Emilia Clarke's (Daenerys) hair extensions are visible in a close up.
When Joffrey has Arya pinned to the ground with his sword and Nymeria bites his arm, the camera cuts to Sansa shouting "Arya!" twice in quick succession. It's the exact same clip used both times.
(at around 12 mins) At the blacksmith's, as the bellows open and close, the sound of the fire roaring comes when the bellows open to take in air rather than when they close to push air into the fire.