When Homer begins to imagine what the Winter Olympics are like, he's wearing a curling sweater. On the close up when he snaps out of it, he's wearing his usual white collared shirt. The 'camera' then pans out and he's wearing the sweater again.
When Seymour Skinner is walking up to the table to sign the Olympic forfeiture document the other team, 3 Olympic officials and Skinner are all standing on a carpet covering two of the four curling lanes. When he steps up to the table to sign the document only one lane is covered and Skinner is the only one standing on it.
When Bart starts cutting out part of Homer's face from his license, he is pictured wearing a smile. But when Bart sets the cutout down on the table, he is suddenly wearing a frown.
After the winning and final throw, the shot changes several times as they celebrate, and the number and position of stones on the target changes with each shot change.
During the Olympic opening ceremonies, the the first country to be introduced was Albania. In every Olympics, Greece is the first country to be introduced because they hosted the first Olympics.
The sign outside the ice rink proclaims the day as Thursday: Clockwise Day. Homer later complains that the curlers come to sweep the ice on Saturday. Later, during his poetic speech after being invited to curl, he says it is the 17th of November. Since they are in exhibition for the 2010 Olympics, it is reasonable to assume that the story starts in November 2009. The 17th was a Tuesday in November 2009.
Women pole vaulting was only made Olympic in 2000.
Agnes is talking about her pole vaulting career when she was pregnant and Seymour kicked as she vaulted and kicked the bar down, Seymor is agreeing but in reality he is not the real Seymour Skinner but Armin Tamzerian so he wasn't actually in Agnes at the time.