Continuity mistake: Toby and Leo are in Leo's office talking about the friendly fire incident - Leo's glasses are sitting on his desk in front of him. He then picks them up and moves them to the far left. A couple of shots later, he picks them up from the right and puts them on.
Continuity mistake: While Sam and Donna are listening to a TV report that Sam may be heading for Congress, the woman behind him has a phone receiver to her ear, with both hands on the phone. The shot changes and suddenly her right arm is down by her side, but in the next shot it is back in the first position.
Factual error: In the scene when Leo tells president Bartlett that he is attending the concert, they refer to the Icelandic ambassador as a man. Leo says his name is Vigdis Olafsdottir, when is fact it is a woman's name that means Vigdis daughter of Olaf. During the concert the ambassador is portrayed by a man. They "borrowed" this name from Tom Clancy's novel Red Storm Rising, by the way.
Continuity mistake: During the beginning before the opening credits, C.J. is briefing the press corps on the bus. In the outside shot of the bus, C.J. has her left arm resting on a rail, towards the door. When the shot changes to inside, C.J. has her right arm on a rail towards the driver. (00:01:15)
Audio problem: During the blackout, Donna and Josh sit together. The scene begins with the camera looking out the window, panning right to reveal Donna as we hear her finish saying, "You know what I'm surprised about?". But her mouth isn't moving at all until she begins her next sentence, and it's visible when we're hearing "about". (00:36:00)
Continuity mistake: Leo enters the situation room and is told the "planes are on the deck". He watches a video feed as a plane is launched from the USS Lincoln. The S3-B Viking is seen approaching one camera (single vertical tail fin, wing-mounted engines), then from another angle, we see an F-14 Tomcat lifting off (dual tails and fuselage-mounted engines) and moving away from camera. This is supposed to be live video, and it isn't possible two different jets are launching from the same carrier at the same exact moment, so it can only be a bad choice of stock footage by the show's makers. (00:38:55)
Continuity mistake: Josh is getting coffee and talking to another guy about a Shakespeare production Bartlet is supposed to attend. When he goes to the coffee machine, his backpack is over his shoulder and the strap is near his collar but not covering it. When he walks away from the coffee machine, most of his collar is covered and quite dishevelled from the backpack strap. At no time did Josh adjust the backpack.
Continuity mistake: After President Bartlett sits down (while speaking to CJ and the staff) he removes his glasses. The shot then changes to one from his back where he's wearing glasses. When the angle changes to the original, he's not wearing his glasses again. (00:06:30)
Continuity mistake: When the guys arrive outside Donna's building, Josh wears a tux and a long black coat with a white scarf. After Josh says, "The buzzer's not working", a few quick camera cuts occur, and as he says "Nah, I know women-" and turns, the scarf is missing. It is back as the cameras cut again and he says, "I know what they like." (00:33:30)