Toby says that Bartlet must carry "the Northeast, Pacific Coast, and Industrial Northwest" to win re-election. There is no such area as the "Industrial Northwest" - perhaps he meant "Industrial Midwest".
President Bartlet asks a teacher if she taught "Beowulf" in the original Middle English or in translation. Bartlet, an established know-it-all, would have been aware that "Beowulf" was written in Old English in the 8th century, some 200-300 years before the language had evolved into the form now known as "Middle English".
When the HUD Secretary is talking to Toby he says "If this announcement makes A17 of the Metro section I'd be surprised." The Washington Post's Metro section is actually section B and almost never has more than 10 pages.
When President Bartlett is filing Charlie Young's tax return for him, it is noted that he was expecting $700 back and it came back saying he owed $400. This would have been highly unlikely as it is noted in previous episodes he is raising his sister. This would mean he would be eligible for the Earned Income Tax Credit, which would result in him receiving much more money back. As President Bartlett says he likes doing this and he has a noble prize in economics, and does his own, he would know about this as he has three children. The reference of the rebate also referred to as an advance by Charlie, wouldn't have made that much of a difference in regards to the Earned Income Tax Credit.
The goof item below may give away important plot points.
Near the end of the episode, when Donna comes into the Oval Office for the conversation with Mrs. Morello, President Bartlet says that General Pulaski commanded "our calvary during the American Revolution." He should have said "cavalry".