While CJ is telling the President about Zoe lying to the reporter, the door she enters from is not shut completely when they stand up, but it is when she leaves.
Jed Bartlet when reading from George Washington's Presidential Behavior Jed says "When in Company, put not your Hands to any part of the body, not usually covered" But it actually says "not usually Discovered" which changes the line completely.
Jeff Breckenridge says his African ancestors were kidnapped and taken to New Guinea before being shipped to the USA. New Guinea is in the Pacific ocean north of Australia, and he should have said either Guinea, Guinea-Bissau, or Equatorial Guinea, all of which are in Africa.
CJ refers to Zoey as the First Daughter. As She is the youngest, of three, Zoey would be the Third Daughter, as she points out herself to Penn and Teller later in the series.