Character mistake: Will's tax demonstration to his volunteer staffers is incorrect. He applies the various tax rates to the entirety of each salary range. The person who makes $150K and is in the 36% rate...in his example he has them paying 36% on their entire salary, not just the portion of it that puts them ahead of the next lower tax rate. If the tax rate jumped to 70% at income of $1M, and a person earned $1,050,000, they wouldn't be paying the 70% rate on all $1,050,000 of their income, only the last $50,000 of it. Will's example makes it look like they would be.
Continuity mistake: Bartlett is in the executive office in the residence watching four TVs at once. He hears a line in the black and white movie, a second later he rewinds it to hear the line again - he rewinds way too much and for too long, but once he stops the tape, it plays the line he wanted to hear again right away. He went too far back (for visual effect) than what in reality it would have taken.
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.
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)
Factual error: 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. (00:13:05)
Continuity mistake: Near the beginning of the show, Josh is talking about baseball while looking at some stapled political papers - the top one is folded back over the second one. As Donna asks "what is it?", the first page is falling free and Josh is only holding the second one, but he had no time to adjust them.
Continuity mistake: Bruno and C.J. sit down in a meeting and are talking about women voters. When the shot is on Bruno, we can see C.J. is holding a black folder that is partially open. When the shot goes to her, though, she has her hands on the folder, which is opened on the table.