After his speech prep, President Bartlet is speaking to Leo about the language in the speech, and then goes on to explain he had to look up Kundu in an atlas after getting a security cable that morning. This is odd, since the President had met with the president of the REK in Season 2 in the episode entitled In This White House (2000).
The opening screen shows that Inauguration Day is Sunday. According to the 20th Amendment the formal, public Inauguration Day is moved to Monday when it falls on Sunday. A private swearing-in may still be conducted on Sunday.
In reference to LCDR Reese's dress uniform, it's mentioned more than once that there are 13 buttons on the trousers. Only the Navy enlisted dress blue uniform has 13 buttons on the trousers, none of the Naval officer dress uniforms do.
When Will Bailey is researching President Bartlet's past speeches, he sends for them from the New Hampshire State House, which is in Concord. Later the boxes arrive from Manchester.
During his conversation with Asst. Secretary of State for Public Affairs Brice Lilley, Will Bailey refers to the non-existent "clause in Article One that says not every president gets the full powers of Commander-in-Chief." Article One deals with the creation of the Legislative Branch. Any clause dealing with presidential powers would be in Article Two, which deals with the creation of the Executive Branch.
When Donna is describing Jack's uniform one of the awards she mentions is the Bronze Cross. That should be the Bronze Star. She also says his pants have 13 buttons. Only Navy enlisted "bell bottoms" have/had 13 bottoms.
Leo talks about British Magistrates wearing wigs. They don't, but judges (in higher courts) do.