In the Shadow of Two Gunmen: Part I - S2-E1
Factual error: In the scene where the Secret Service chief is in the car with Bartlet and he suddenly realizes Bartlet's injured, he yells to the driver to get to GW Hospital and the limo does a screeching U-turn on what appears to be the Arlington Memorial Bridge. At the time they were supposed to be heading from Rosslyn, VA, where the event was, back to the White House. But GW is in DC, not that far from the White House, so although the U-turn looks cool, it doesn't make geographical sense. Also, in that one shot of the outside of the car, it appears to be pouring, while back at the scene of the shooting as well as ahead of them at the hospital entrance, it's not.
Suggested correction: At the point where we see the Lincoln memorial, we're given the first hint that it is the Arlington Memorial (and not the Roosevelt). But they're almost off the bridge at that point and it's a full 1 minute and 6 seconds later that he yells for GW. The turnaround wasn't on the bridge. Given that amount of time, they could have been most of the way down Constitution Ave NW. (or any other side street) heading away from GW and heading to the White House. A turnaround would make sense.
Continuity mistake: The President is watching Dial M for Murder with the staff and his daughter Ellie. In the beginning of the scene, the President is sitting behind Ellie and there is no empty chair next to her. Then he leaves the room. When he returns, his chair is suddenly placed next to Ellie.
Suggested correction: There was an empty chair next to her.
Somebody's Going to Emergency, Somebody's Going to Jail - S2-E16
Character mistake: In this episode the Organisation of Cartographers for Social Equality claims the cartographer Mercator is German. He is in fact Belgian. He was born Rupelmonde Belgium, March 5, 1512 and died at Duisburg Germany, December 2nd, 1594. (00:24:00)
Suggested correction: Although Mercator was born in Rupelmonde, it was during a visit his parents were making to the town. His family was ethnically German, as they came from Gangelt in the Holy Roman Empire. This is also where Mercator spent much of his adult life (specifically in the German city of Duisburg). Calling him German is technically correct.