While Leo and Admiral Fitzwallace are watching the kidnapper's broadcast of Zoe holding the day's newspaper, the camera sweeps the room to reveal a map of the Middle East. This map omits the existence of the nation of Qumar, showing the real-world political borders of Iran.
In the 5th Season, Ryan Pierce became an intern for Josh Lyman. Ryan claims Franklin Pierce, 14th President of the United States, is his Great-Great Grandfather, however, Pierce never had a son live past 11 years old.
When Josh confronts Steve Atwood in the men's room, Steve flushes the urinal and the valve and water supply pipe wobble around, obviously not actually attached to anything. However, if the pipes aren't connected in a certain way, they will wobble when used. Especially in older buildings.
In the scene where the kidnappers' message is being played in the situation room, the Arabic message is actually Abdul Shareef's dialogue from Season 3 when he met with the president, re-used. The producers simply gave a different translation.