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.
Twenty Five - S4-E23
Other mistake: Chairman of the Joint Chiefs Admiral Fitzwallace tells Bartlet that he wants to attack targets in Qumar. The first he mentions is "the Bahji C3I" which he explains is "Communications, Command, Control and Intelligence." The explanation shows the actor John Amos flubbed his line and should have said "the Bahji 3CI", as in "C.C.C.I" or "Triple-C I." This is common governmental and military abbreviation jargon, much as the show often uses "D-triple-C" to mean the D.C.C.C. (Democratic Congressional Campaign Committee). (00:16:50)
Suggested correction: C3I is similar to C2, pronounced "C two" and commonly used in military to refer to command and control.
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.
Election Day (Part 2) - S7-E17
Trivia: The election originally ended with Arnold Vinick as the victor. But in light of John Spencer's death (and by necessity, Leo's), the writers felt it would be too emotionally taxing on the audience for Santos to lose both his running mate and the election.
Suggested correction: The writers were not certain if they wanted Vinick or Santos to win, but it was not decided by John Spencer's death. They shot the scene in the thirteenth episode with John Spencer, indicating that it was decided well before his death that they wanted Santos to win. The direct quote "it would be too emotionally taxing on the audience for Santos to lose both his running mate and the election" is true, but said in the context of a decision being made independent of the death and subsequent character death.