President Bartlet says that the Manchester, NH school district has about 1,100 kids in it. That is more appropriately the size of the Manchester, MA school district, a district in a small town that does not even have its own high school. Manchester, NH is the largest city in the state and has 3 public high schools, each school having far more than 1,100 children in it. In fact, the Manchester, NH school district has well over 11,000 students in it. A New Hampshire native, as Bartlet is supposed to be, would definitely know this.
Sam convinces his law school classmate, Tom Jordan, to run for Congress. Later, the White House staff learns that Jordan struck potential jurors merely because they were black. Both Sam and Leo McGarry refer to these as "preemptive" challenges, even though the correct term is "peremptory." While Leo might have made this mistake, an attorney like Sam would never have referred to them as "preemptive" challenges. Furthermore, although the two words sound similar, they are not synonyms; "preemptive" means "intended to preempt or forestall," whereas "peremptory" means "having to be obeyed without question."
Congressional candidate Tom Jordan is described as a graduate of Oberlin College who lived in an all-white fraternity. Oberlin College hasn't allowed its students to join fraternities since its founding in 1833.
When President Bartlet and Toby are talking, the President says that the West Virginia white supremacist group is based in a diner in Blacksburg. There is no Blacksburg, West Virginia; there is a city in Virginia by that name, and it's not too far from the West Virginia state line, but it's unlikely that a West Virginia group would be using a diner in Virginia as its base of operations.
Sam claims to have gone to four different schools at different points. In the first episode, when speaking to Malory's class, Sam says that he is a graduate of Harvard and Yale. Later, in the episode where Ansley is hired, Sam tells the White House counsel that he was recording secretary of the Princeton Gilbert and Sullivan society. Finally, in the first midterm elections, when Sam is trying to convince his old classmate to run, they talk about a professor they both had at Duke law school.
In the final scene, Sam informs Josh, C.J. and Toby that of the 12 House races, "in none of them, did the incumbent win. In none of them, did the party that previously held the seat win", that Republicans won 7 out of the 12 races keeping the House the same as it was before the Midterms. It may seem as if the incumbents had all lost, it would have been the Democrats to have won 7 of the 12 races and the House would not have stayed the same. However, they are not referring to the number of seats when they mean change but who is in control of the house. If the democrats needed more seats than they had one to gain control, then the house would not have changed even if they picked up more seats. Also, a party that is in control may have less seats up for re-election during a given year so the assumption that the republican controlled house would have 7 seats of the 12 prior to the election is not correct.