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.
Other mistake: During the peace talks between the Arabs and Israelis CJ tells the press that the group had Maryland Crab Cake for lunch. Jews would not eat crab and some Muslims also would not.
Transition - S7-E19
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. (00:12:45)
Continuity mistake: When Toby and Josh meet with Judge Ashland, a teacup and teapot appear in front of the judge without either him or anyone else putting them there. (00:20:20)
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)
Factual error: Near the end of episode 1 in series 6, General Alexander is briefing Leo, and the screen shows the Alpha strike headed east toward Syria from the USS Lincoln, which is depicted as being in the Mediterranean. In episode 2, he briefs the press, telling them that the strike was launched from the Lincoln in the Gulf.
Factual error: In the first shot after the recap, the overlay text reads "United States Capitol/Sunday/Inauguration Day". During this episode and the one that follows there is an inauguration day celebration and President Bartlet makes his inauguration speech. Historically, however, when inauguration day falls on a Sunday the celebrations and speeches are scheduled for the next day, a Monday. The president is still sworn in on inauguration day (March 4th until 1933, January 20th after that), but all other activities are moved back one day. The inauguration date has only fallen on a Sunday 6 times since 1798, and only twice since the current inauguration date was set, so it is understandable that this arcane but important bit of scheduling tradition was missed by the show's researchers. (00:00:45)
Character mistake: While in the Situation Room Leo says twice "we need the calvary." According to Webster, calvary is a proper noun that refers to the hillside on which Jesus was crucified. Cavalry is a group of highly mobile army troops. Leo meant to say "cavalry" but mispronounced it. The subtitle is correct with the spelling "cavalry." Leo would definitely know better. (00:19:00)
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.