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.
In the Shadow of Two Gunmen: Part I - S2-E1
Revealing mistake: When the Secret Service drags Hoynes out of the White House lobby, they exit through the main entrance, doors that are shown in episodes before and after as leading directly outside. But instead of seeing a convincing night exterior this time, the flashing cameras reveal nothing but a blue studio backdrop is out there. (00:06:30)