When Nancy briefs Leo, she identifies the USS Portland as a Seawolf-class submarine and notes that two other Seawolf-class submarines stationed "off Japan" would be in position to affect a rescue mission. While it is true that the US Navy has three Seawolf-class subs, in 2001, only two had been built, as the USS Jimmy Carter was still under construction.
Dr. Bartlett tells Oliver Babish that the lawsuit was dismissed by New York Superior Court Judge Ngyuen. There are no courts in New York called Superior Court. The equivalent to a Superior Court in New York State is called the Supreme Court.
When Albie Duncan is having a meeting with President Bartlet and McGarry, he pronounce the "I" in "casus belli" as you pronounce it in the word "Iowa". That letter is to be pronounced as in the world "Indiana". It is strange that President Bartlet, who speak Latin and never lose an opportunity to do a bit of show-off about his vast knowledge, should let that go.
Albie Duncan refers to the Hughes Glomar Explorer as the USS Glomar. The Explorer was not a Navy warship, so it would not have the designation USS. When the ship was eventually transferred to the Navy reserve fleet, it received the designation USNS (US Navy Ship). Glomar was the abbreviated name of the Hughes Global Marine Development Corporation.
When the USS Portland calls in near the end of the episode, she reports her position as "36.6 North, 110 West." This would put her not in North Korean waters, but in the desert of northeastern Arizona.
The USS Portland captain mentions maintaining radio silence to evade a Luda class destroyer. This class is only employed by the Chinese People's Navy, and would not be actively patrolling North Korean waters in the first place, let alone be so close to the South Korean border.