Goofs

Yoren states that they have to travel "a thousand leagues" from King's Landing to the Wall. Depending on the exact measurement of a league (varying from 3 to 3.45 miles in English-speaking regions), this would amount to a journey of at least 3,000 miles. The continent of Westeros, measured from the Wall to the southern sea, is said to be less than 2,000 miles. The journey from King's Landing to the Wall would be around 1,000 miles, so either Yoren's statement is way off, or a league is measured differently in Westeros.

At the end of the episode, when the Dothraki all kneel after Daenerys stands up, the men behind her next to the horses drop completely on the ground. However, in the wider shot of the scene, the men are still standing with just their heads down. When the final shot is widened further, some of the men near the horses have disappeared.

After Ned is beheaded, his sword Ice is covered in blood much more than should have been, given that his neck was sliced cleanly and swiftly.

While accepting that it's a fantasy world, the top speed of a raven is around 25mph. Even if 1,000 leagues equates to 1,000 miles (and miles are referred to elsewhere), that would take 40 hours non-stop flying, yet raven news appears to arrive at all points of Westeros almost immediately.

Varys says, "I must be one of the few men in the city who doesn't want to be king"; the correct grammar, which he should know, is "don't" (since "who" refers to the few such men).