White House Chief of Staff Leo McGarry is talking to the president and says of Iceland's Ambassador, Vigdis Olafsdottir, that "he's very excited to meet you". An Icelandic name finishing in "dottir" is a woman's name (men's names end in "son"), so the Ambassador can't be a he. (In addition, Vigdis is a female forename). Iceland's president from 1980 to 1996 was Vigdís Finnbogadottír - Leo would know this.
There is an explosion in Russia. during a briefing Leo asks if it is "in the Oblast region". "Oblast" in Russian is a administrative unit of the country. There are a lot of oblasts in Russia. So, asking "is it in the oblast region" is equivalent to asking "is it in the state region" or "in the county region" without meaning any one of them.
At the Mars briefing rehearsal, President Bartlet states that the temperature on Mars ranges from 15 degrees to -140 degrees. C.J. looks at notes and says that he is wrong, it ranges from 60 degrees to -225. The President says he converted TO Celcius in his head, but that is converting to Fahrenheit (approximately).
There is no Reykjavík symphony orchestra, there is the Icelandic symphony orchestra and it has it base in Reykjavík.
In the Situation Room, when the President is being briefed on the russian missile silo incident, Bill Clinton's official portrait is hung on the wall instead of Jed Barlet's.
The concert programme is improbable, compiled by someone who doesn't go to classical music concerts. A visiting orchestra will often play a work by a composer from the host country, but Barber's Second Symphony was suppressed by the composer, and is rarely performed. There is no work by Stravinsky called 'Variations on a Theme' - it could be 'Variations: Aldous Huxley in memoriam'. Schoenberg's Verklärte Nacht, being for strings alone, is unlikely for a tour, where the whole orchestra would be used as much as possible. On tour, an orchestra wouldn't bring a work by a 'new' composer - they would be fairly well-established in their own country, and unless there was to be much rearrangement of the platform for this piece, a new work is generally played in the first half, so the audience doesn't leave before it.
When C.J. Cregg asks Toby Ziegler how many moons the planet Mars has he responds by saying two, and that they are named for the horses that pulled the god Mars' chariot. This is incorrect, Deimos (dread) and Phobos (fear) were the sons of Mars, or more correctly of Ares.
While speaking with the Russian Ambassador President Bartlet refers to Minsk as if it were in Russia. Minsk is the capital of Belarus.
White House Speech Writer Sam Seaborn disparages the introduction a NASA public affairs person has written by responding to the man saying "we're both writers" with "if we broaden the definition to those who can spell". Sam then rewrites the introduction and it begins "... you, me, and... are going to..." The correct pronoun is "I" and not "me" (remove the others from the sentence and see if you'd still say "me").
Bartlet says that "NASA is great at naming things" and then proceeds to list various NASA programs and spacecraft but finishes with "the Sea of Tranquillity" and "the Ocean of Storms," names that have been given to those lunar areas since early telescopic investigation in the 17th century.
UR-100N/SS-19 missiles do not use hydrogen as fuel. Instead they use asymmetrical dimethylhidrazine for fuel, and nitrogen tetraoxide as oxidiser. Even if it did use hydrogen, (which is extremely difficult to contain long term) the fuel would not be stored on the missile and therefore could not be offloaded.