According to the novels, Cersei never gave birth to a child of Robert. As she revealed to Eddard, she was once pregnant with a child of Robert, but had the child aborted out of hatred for him. Robert was unaware to both the pregnancy and the abortion.
After the events in this episode, Lady, real name Zunni, was adopted by the actress Sophie Turner, who played her owner Sansa Stark.
While filming the early episodes of season 1, Lena Headey was pregnant. You can clearly see her "concealed" bump at the end of this episode during the aftermath of the direwolf incident.
The episode title refers to the longest and grandest highway in Westeros, running from Castle Black at the Wall all the way south to the capital city of King's Landing, passing Winterfell along the way. Many of the characters, among them Eddard and Jon, travel on this road throughout the episode.
According to writer George R.R. Martin, the Wall, which was created to protect the rest of Westeros from invasions from the north, is based on Hadrian's Wall, a man-made fortification in northern England. Although the real-life structure was considerably smaller (73 miles wide, 12 feet tall) than its fictional counterpart (300 miles wide, 700 feet tall), it served the same function: protecting Roman forces in England from barbarian tribes in the north. Hadrian's Wall also had forts set at regular intervals along its length, and soldiers were sent from all over England to man them.