When Benjen goes to talk to Ned at the feast, his hair is shorter and styled differently than when he talked to Jon just a few minutes earlier. This is because the feast shot was one of the few shots from the unaired pilot episode, that was used in the first episode.
After the wedding, Drogo places Daenerys on her mare, on a side-saddle. However, the next shot shows Daenerys sitting on her mare astride, with no time for her to have moved to that position.
While being presented to Drogo as his future bride, Daenerys walks past Viserys twice.
When the camera pans over the dead stag, its horns are intact. But when the camera shows the dead direwolf, one of the very same stag's horns is embedded into the direwolf.
When Ned is talking to Robert towards the end of this episode, the light on the side of Robert's head appears and disappears between shots.
Cat and Ned both have blue eyes. While it is not completely impossible, the probability of two blue-eyed parents having a brown-eyed child is less than 1%. The probability of them having more than one brown-eyed child, basically zero.
In the first scene with Daenerys and Viserys, a mural on the back wall depicts a naval battle with ships firing their broadside cannons. However, there is no known cannon technology yet in Westeros.
The deserter saw the white walker north of the wall, but was apprehended south of it. Since he had no equipment to climb the 700-foot wall, he couldn't have gotten past it except by returning to Castle Black.
In the opening credits of the first two episodes, when the names of the actors appear next to the crest of the House their characters belong to, Emilia Clarke (Daenerys) and Iain Glen (Jorah Mormont) are shown with a Lannister lion, while Sophie Turner (Sansa) is shown with a Targaryen dragon. From episode 3 on, the actors' names appear next to the proper crests (a dragon for Clarke, a bear for Glen, and a wolf for Turner). This was corrected in the DVD/Blu-Ray release.