Continuity mistake: Season 7, episode 2, "The Mommy Problem." At the end of the episode, when Matt Santos is approaching his fighter jet, the number "15" is on the left part of the jet's nose. Later, when the jet is taxiing towards take-off, the number changes to "01".
Factual error: When the president signs Toby's Presidential Pardon you can see his name listed as "Toby." However such a document would refer to someone by their full, legal name. In this case the document should say "Tobias" not Toby, which, although commonly used throughout the series, is still only a nickname.
Continuity mistake: When Bruno and Bob are poring over exit polls, they mention that Santos seems to be leading in North Dakota, and comment that it is a state that hasn't gone Democratic in forty years. While that is true in the real world, in the fictional West Wing world, it is stated in Season 4 that Bartlet won the Dakotas in his landslide reelection.
Factual error: Early in the episode, when Abby complains about who in their right mind would schedule outdoor inaugurations in January, Jed retorts by listing Jefferson, Adams, and Franklin, but inaugurations were in March until 1936 - not a mistake President Bartlett would make.
Continuity mistake: About 18:59. Right after Josh hugs Annabeth, she gives him a cell phone to talk to the White House. In the shot from behind, you can see that he is holding the phone backwards with the screen facing out. When they go back to this shot (after a shot from the front), he is holding it properly.
Factual error: At the end of the episode, a chamber music ensemble plays at the White House. One of the close-up shots is of the oboist as well as the sheet of music on her stand. The music on the stand is not the same piece as that being played, and it's not even an oboe part, but rather a piano score of some solo instrument piece, as can be told by each system having three staves, two of which are bracketed together.
Continuity mistake: After Louise Thornton leaves the Democratic media consultant meeting, Josh runs after her inside the Santos campaign HQ. At some point he talks to her while catching up on her and ends the shot walking ahead of her. In the very next shot, he is again behind her, walking at a fast pace to catch up.
Continuity mistake: Josh comes back from his trip to visit Sam. He walks in the door and lets his bags drop on the floor. He collapses on the couch with his arms spread wide. Immediately, there's a knock at the door and he opens his eyes. When the angle changes towards the door showing him going to get up, his arms are now crossed above and behind his head resting on the couch arm.