Other mistake: I call this one an "Escher Mistake". As Donna and Josh near the end of their chat about the chair that needs repairs, they pass an office door on their left (Nancy McNally's office) just before going through another doorway. The camera that follows them passes "through" a solid wall and emerges in an office, facing a hall and stairwell as Josh and Donna enter from our left as if this has all been a continuous shot. But the camera-through-the-wall moment is actually a cut so that the actors can be on a totally different part of the set. This would be fine, except the staircase they are about to turn left to and climb only rises up about 3 feet, then the user turns left again and heads to our left - but that sends the user into McNally's office, and does so 3 feet off the floor, yet they are seen entering the press room instead.
Other mistake: As Donna and the photo-journalist are about to leave the checkpoint, they each shake the soldier's hand. Just before the journalist passes in front of the soldier, the soldier goofs and looks directly into the camera, then catches himself and instantly tries for a 'thoughtful gaze' at the ground.
Other mistake: CJ is in Dayton, Ohio visiting her father. She is in the middle of her high school reunion speech when Toby calls from the West Wing. It is light in D.C. outside Toby's office window, but CJ is giving her speech at night when it's dark out.
Other mistake: In a scene with Leo and the President, Toby confronts them about the fact that there was no clear person in charge while the President was in hospital after being shot. He references the shooting as taking place 'last May'. However, in an earlier episode, 'The Midterms', there is a title card that states the date as August 14th and in the scene that follows there is discussion about the staff job approval in which CJ states, 'A week ago the job approval is at 51, we got shot at and its at 81.' This would mean that the shooting took place in August not May.
Other mistake: Chairman of the Joint Chiefs Admiral Fitzwallace tells Bartlet that he wants to attack targets in Qumar. The first he mentions is "the Bahji C3I" which he explains is "Communications, Command, Control and Intelligence." The explanation shows the actor John Amos flubbed his line and should have said "the Bahji 3CI", as in "C.C.C.I" or "Triple-C I." This is common governmental and military abbreviation jargon, much as the show often uses "D-triple-C" to mean the D.C.C.C. (Democratic Congressional Campaign Committee).