Genius Bonus: When President Zia asks Charlie if he has the authority to make these deals, Charlie replies that he has none, and is pretty close to violating the Logan Act. Although the delivery is funny, it's ten times funnier if you know that the Logan Act was passed back in 1799, and forbids unauthorized persons from negotiating with foreign governments. The comedy is that the Logan Act is so incredibly vaguely worded that no one has ever even been prosecuted for violating it, let alone convicted, in the last 214 years. It's a measure of how far beyond his authority Charlie is going, that this is actually on his mind.
Hilarious in Hindsight: Late in the movie, Cravely is dressing up as Santa Claus for an office party. John Slattery, the actor who plays him, plays Roger Sterling on Mad Men, where he also had to dress up as Santa for a Christmas party one time.
One-Scene Wonder: Technically two scenes, but Ken Stott as Zvi Rafah surely takes some sort of prize - witness the number of quotes from his short appearance on this very page.
Tear Jerker: The scene when Charlie stands in an Afghan refugee camp, and the camera pulls back to note how big the camp is...