The scene where everyone in Winterfell gathers to welcome Robert Baratheon is the only scene in the entire series where the whole Stark family is seen together.
A real dead stag - not a prop - was used for the scene where the direwolf pups are found. The actors found the smell during the filming of the scene revolting, as it had been dead for two days at that point and was decomposing.
Lena Headey was pregnant while filming this episode, so many scenes show her either wrapped in furs, sitting down, standing behind something, or only in close facial shots to conceal the pregnancy.
Sansa named her wolf Lady. Lady was played by Zunni from Mahlek Northern Inuit Dogs. Sophie Turner, who plays Sansa in the series, adopted Lady as her own pet when the first season wrapped and live animals were replaced by CGI.
While most married women in the series take on their husband's last name (like Catelyn and Lisa Tully, who have taken the names Stark and Arryn respectively), Cersei Lannister (who is married to King Robert Baratheon) has not. The reason for this is the rule that the name of the house that currently holds the Iron Throne can only be inherited through birth, and is not given upon marriage. If Sansa were to marry Joffrey, she would still be called Sansa Stark, not Baratheon.