Plot hole: In Season 1, Episodes 5&6, it's mentioned several times that Zoey is already 19 a few weeks before she starts college. Yet in this episode, Charlie points out to Leo and the President later tells Oliver Babbish that Zoey was 17 when she was filling out her enrollment forms for college, therefore a parent had to sign them. These are enrollment forms, not application forms - it's extremely unlikely that they were filled out over a year before she started school.
Plot hole: As Josh arrives at the security gate of the White House, protestors are gathered, chanting and otherwise talking loudly. He enters the gate, makes his way to the north entrance of the West Wing, and as he enters the lobby, the crowd is still heard quite plainly, just as loudly as at the gate, as if they were right outside the door, yet the protestors are much too far away to be heard so loudly, if at all.
Plot hole: In order to allow time for a lengthy scene conversing while walking, actor John Spencer is sent on a ridiculous course through the West Wing. See the floor plan at http://www.whitehousemuseum.org/west-wing/west-wing-TV.jpg to follow along. He's first spotted leaving Margaret's area (blank space located just up and left of his "Chief of Staff" office on the plan). The handheld camera is in the Roosevelt room at this point. He turns right, traveling between his office and the Roosevelt room, meeting Donna along this hall. They make two slight left turns, then a hard left, entering the Roosevelt room (at the top/right corner's diagonal door). They walk the length of the room, turn left (down) and Leo drops some of the paperwork he carries onto the end of the table. They then exit the room (bottom left door) which is right outside the doorway where Leo started the scene. Leo isn't wandering. He's quite deliberate in his choices, yet if he'd simply walked straight ahead 6 or so steps from where he started, he'd have been where he dropped the papers.
Plot hole: The Zoey Bartlett kidnap crisis cliffhanger that stretches across the end of Season 4 and the beginning of Season 5 makes no sense in terms of time. Charlie pulls out a note from his wallet that says they will dig up a bottle of champagne on May 7 - Zoey's graduation night. They do. Later that night she is abducted. She is gone three days. Four days later (in "Jefferson Lives") Abby chews out Leo, saying, "It's only been four days and her bruises have not yet begun to heal." The date should be May 14th. However, "Jefferson Lives" supposedly occurs on the Fourth of July - Zoey says it's the Fourth and they all watch the Capitol Fireworks at the end. Boy, that sure was a short month of June.
Plot hole: The fighter jet alongside Air Force One has "NY" tail markings which designate it's with the 174th fighter wing, with a home base of Syracuse, New York. Surely, in this emergency over Washington, DC, jets from a more local base (like the 113th's F-16s at Andrews AFB) would have been dispatched to aid the President's plane.
Plot hole: Joey and Kenny are led to the Oval Office by Charlie through the Presidential Secretary's (and his own) office. Charlie ends the scene saying, "Okay, you're in the Oval Office" as he sends Joey and Kenny that way. Charlie always knows the President's whereabouts and schedule. Yet moments later, Josh arrives in Leo's office where others have gathered to await the start of the same meeting - and Joey and Kenny are also here. Then everyone goes into the Oval Office to await the arrival of the President. It is as if the makers forgot Charlie led Joey and Kenny here moments earlier.