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: 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. (00:28:00)
Factual error: When Sam is telling Leo about the couple who crashed their car after the fundraiser where the President talked about seat belts, he states, "Now she's suing him for contributory negligence!" Contributory Negligence is not something you can sue for, it is a defense to a lawsuit and is based on the plaintiff's own negligent conduct - the woman would be suing the president for just "negligence." Sam repeats the phrase at 7:45, when he claims "Contributory negligence in wrongful death is the tort equivalent of murder." This makes no sense from a legal perspective. As an attorney, Sam would know the difference - this a writing mistake. (00:01:52)
Factual error: When President Bartlet is on the phone with the butterball hotline, he claims to be from Fargo, ND. Charlie tells him the zipcode of Fargo is 50504. Fargo has 13 zip codes assigned to it. None of them are 50504. They are all beteeen 58102 and 58126. (00:28:05)
Factual error: When Leo is talking with Jordan about why he doesn't want the President to be censured, he states that this would be the first time a President was censured. This is untrue. Both Andrew Jackson and James Buchanan were censured by Congress (although Jackson's censure was later expunged). (00:11:25)
Factual error: Lord John Marbury says he is "the Earl of Croy, Marquess of Needham and Dolby and Baronet of Brycey." His title according to the British peerage rules would be "The Earl of Croy" and he would be called Lord Croy in conversation. Lord John Marbury would be what one of his younger sons also named John would be called.