Factual error: The Lockheed 1011 was only produced until 1984. There's no way that in 1999 Toby would be flying on one that "just came off the line 20 months ago."
Factual error: When Leo is reminding the Congressional Aides about their bosses' drug scandals, he states that Vicodin is a Schedule II Controlled Substance. At the time the episode was shot, Vicodin was a Schedule III Controlled Substance. Given his experience in this area he'd know better.
Continuity mistake: When Toby is walking back to his office from the press room with his ex-wife, the ex-wife's tag and chain keeps changing through the entire sequence. Sometimes it's over her jacket and the tag's just hanging or it's under the jacket and the tag is sitting just inside her jacket.
What Kind of Day Has It Been? - S1-E22
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. (00:11:50)
Post Hoc, Ergo Propter Hoc - S1-E2
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)
Character mistake: During the face-off about religion/politics, they get into a shouting match about commandments, both groups being equally convinced that "honour your father and mother" is the 1st or 3rd commandment, respectively. In actual fact it's the 4th or 5th, depending on which version (Catholic or Protestant) of the 10 commandments you go by. See http://www.positiveatheism.org/crt/whichcom.htm.
Character mistake: Sam makes a joke about Laurie being "free of cataracts" because she smokes so much pot. She laughs and says "I get that. That's funny." Except there's nothing to 'get', because Sam is wrong. Cannabis has been used as pain relief for people suffering from glaucoma; it does nothing whatsoever for cataracts. It's surprising that neither Sam nor Laurie would have known this. (00:03:10)
What Kind of Day Has It Been? - S1-E22
Continuity mistake: When the shooting starts, CJ is seen being pushed down by a Secret Service agent, and a second later she is seen being pushed down by Sam.
Visible crew/equipment: When Donna opens Josh's Christmas gift, actor Bradley Whitford's mic pack is visible on screen tucked behind his belt. (00:37:55)
A Proportional Response - S1-E3
Continuity mistake: When Leo asks Chairman of the Joint Chiefs Admiral Fitzwallace about the optics of hiring Charlie, a black man, to carry the president's bags, Fitzwallace's ribbons on his Navy uniform are upside-down. This mistake is very visible because he has two ribbons on the bottom when there should always be three. On his way out the door, there is one shot where Fitzwallace's ribbons have been fixed, but then as he walks out the door his ribbons are upside-down again. (00:25:50 - 00:27:10)
Let Bartlet Be Bartlet - S1-E19
Factual error: In the Don't Ask Don't Tell meeting, the USAF Major is wearing a JCS service badge on his right. That is the position for females. It would actually be worn below his ribbons. He is also not wearing a name tag on his blue shirt after he takes his jacket off. That is the one mandatory item required on his shirt.
Six Meetings Before Lunch - S1-E18
Character mistake: In this episode, the character Jeff Breckenridge meets with Josh to plan his Senate confirmation. When explaining what led him to be a civil rights lawyer, he tells how his great grandfather was captured into slavery, and "taken to New Guinea to be shipped to America". The character probably means Guinea, or Guinea Bisseau, or Equatorial Guinea, three places in the Western coast of Africa from which black slaves were sent to America. New Guinea, on the other hand, is half-the-world away, near Australia.
A Proportional Response - S1-E3
Continuity mistake: The president is snapping at everyone while looking for his glasses. Newcomer Charlie addresses Bartlet, who turns and takes off CJ's glasses he'd been trying on. Everybody freezes in surprise at Charlie's interruption, including Bartlet who can be seen holding the glasses away from his body. In the immediate next shot, Bartlet can be seen on the monitor still wearing CJ's glasses, and then interrupts Charlie while removing the glasses once more. (00:33:20)
Continuity mistake: When Josh and Leo are discussing Leo's alcoholism Josh refers to Leo as being "Boston Irish-Catholic" but in several other episodes it's mentioned that Leo is from and grew up in Chicago.
Let Bartlet Be Bartlet - S1-E19
Continuity mistake: When CJ leaves Toby's office and Josh sits town on the couch next to Toby she closes the door as she walks out and we can hear it close. But the camera switches to a different angle as Josh sits down and the door frame is still in picture and is open as we hear the sound of it closing the door frame is still open. (00:20:40)
The Crackpots and These Women - S1-E5
Other mistake: When the President and his staff stop preparing for his upcoming press conference they decide to meet again "this afternoon" implying that it is still morning. In the very next scene Sam meets with the representative from United States Space Command he tells Sam that at 6:35 AM local time UFO's were detected over Hawaii. That's not possible. Hawaii is 6 hours behind Washington D.C. If it were noon in Washington, it would only be 6 AM in Hawaii, 35 minutes before the time the gentlemen mentioned.
Take Out the Trash Day - S1-E13
Continuity mistake: This episode takes place in early 2000. 7 or 8 months before the midterm. When Bartlet tells C.J. to drawer the sex education report until after the midterm she exclaims, "next year?"
Take Out the Trash Day - S1-E13
Continuity mistake: This episode takes place in February or March of 2000. Josh and Donna have worked in the White House for 13-14 months, but in the beginning of the episode Donna is asking Josh what 'take out of the trash day' is, when she has been working in the White House for many, many Fridays.
He Shall, from Time to Time - S1-E12
Continuity mistake: When Abby kisses Jed as he's falling asleep there is a change in shot perspective; Abby's hand is suddenly on Jed's chest and the bed sheets move at least a foot towards his head. (00:12:00)
Character mistake: Both in the title and throughout the episode, people refer to 'Lord John Marbury'. However, the first names of peers are not used when also using their titles; so Marbury should be called either Lord Marbury (more accurately Earl Marbury), or just John Marbury. A minor error in the real world, but the White House is supposed to be aware of diplomatic eccentricities like this.
Chosen answer: A really annoying innate lack of sense. My friends and family say the same thing all the time, and I'm endlessly trying to correct them. I think people just don't know any better and (ironically) couldn't care less that they're speaking incorrectly.