Factual error: When Leo is reminding the Congressional Aides about their bosses' drug scandals, he states that Vicodin is a Schedule II Controlled Substance. At the time the episode was shot, Vicodin was a Schedule III Controlled Substance. Given his experience in this area he'd know better.
Factual error: Sam says the "state-of-the-art" oil tanker he recommends can carry 2.2 million gallons of oil and weighs 308,000 tons. The Exxon Valdez could carry over 60 million gallons (1.48 million barrels) and weighed only 211,500 tons. The writers mistakenly swapped 'gallons' for 'barrels' so that this enormous tanker carries very little oil. It would actually carry 2.2 million "barrels", which equals 92 million gallons.
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.
Factual error: When the president signs Toby's Presidential Pardon you can see his name listed as "Toby." However such a document would refer to someone by their full, legal name. In this case the document should say "Tobias" not Toby, which, although commonly used throughout the series, is still only a nickname.
Factual error: In the situation room, Colonel Chase informs Leo that a CH-47 Seahawk helicopter was dispatched from the USS Monterey. Problem is, the CH-47 is called "Chinook" while the SH-60 is the Seahawk (of which the USS Monterey carries two). See: http://picasaweb.google.com/agbeko.Dzamesi/Aircraft/photo5029495094968996146 for photo of an SH-60B Seahawk landing on the USS Monterey.
Factual error: Early in the episode, when Abby complains about who in their right mind would schedule outdoor inaugurations in January, Jed retorts by listing Jefferson, Adams, and Franklin, but inaugurations were in March until 1936 - not a mistake President Bartlett would make.
Factual error: A secret service agent goes to Leo McGarry and tells him Sharif has crossed the border from Canada into the US - he says "from Ontario into Vermont". It is about 50 miles from Ontario to the Vermont border - the only province that borders on Vermont is Quebec. At this high level of intelligence, this could not be a character error - just the West Wing writers not checking a map.
Factual error: When the British Ambassador, Lord Marbury, greets Abbey at her party, he tenders best wishes from "Her Royal Majesty", his Monarch. However, as Her official representative, Lord John should have been cognizant that the reigning British monarch is referred to strictly as "His/Her Majesty".
Factual error: In the Don't Ask Don't Tell meeting, the USAF Major is wearing a JCS service badge on his right. That is the position for females. It would actually be worn below his ribbons. He is also not wearing a name tag on his blue shirt after he takes his jacket off. That is the one mandatory item required on his shirt.
Factual error: In the scene when Leo tells president Bartlett that he is attending the concert, they refer to the Icelandic ambassador as a man. Leo says his name is Vigdis Olafsdottir, when is fact it is a woman's name that means Vigdis daughter of Olaf. During the concert the ambassador is portrayed by a man. They "borrowed" this name from Tom Clancy's novel Red Storm Rising, by the way.
Factual error: Hal Holbrook's character is called in to assist in solving an incident where a US sub has gone missing in hostile waters. Despite being elderly, he is considered an expert in such matters, and is advising the President in that capacity. Yet while relating similar historical submarine incidents, he makes two significant errors. First, he describes the "Glomar Explorer" and the K-129 Russian sub as "two subs", but the Glomar was a surface ship, not a sub (See http://www.espionageinfo.com/images/eeis_02_img0482.jpg). Then he states the USS Gudgeon was trapped by Russian ships for four days, but the entire incident took 30 hours. He is never challenged on these facts, and his advice is unquestioned. Rather than character mistakes, as the character's meant to be an expert, this is more likely bad research and embellishment by the writers.
Factual error: Leo asks how long it will be before the missile system being tested will hit the target, and is told "two minutes, ten seconds". He decides the President should see it, and leaves to fetch him. But doing so results in them both arriving back in the room exactly 3 minutes later. 7 seconds after that, they are told there are still 50 seconds to impact (but it should have occurred 57 seconds ago). After the 50 seconds pass, Leo states the impact will occur in 20 more seconds, and the moment of expected impact does pass at that time. In all, 4 minutes, 16 seconds pass from when "2 minutes, 10 seconds" to impact was announced.