Episode 4.02, Twenty Hours in America Part II, Donna, Josh an Toby are soaking wet when the go into the hotel, but in the next shot, when Toby an Josh have crossed the lobby they and their clothes are completely dry.
The pendulum of the grandfather clock in the Oval Office, never moves.
Sam's office changes from Season 1 to Season 2. It suddenly has a new window.
President Bartlet's code name, in one of the first episodes, is "Eagle." As he passes the Secret Service the agent says "Eagle has passed."
In a episode later that season when Bartlet has collapsed, an agent says "Liberty is down."
First-season scenes shot on location in Washington D.C. show the Washington monument encased in the lighted scaffolding that was part of its renovation process. Aerial views of Washington shown in many of these same episodes (e.g., "Five Votes Down") do not show the scaffolding, indicating that these shots were taken from stock footage dating before the renovation.
In a couple of instances, Secret Service agents are seen holding an umbrella for a protectee. In reality, Secret Service agents must keep their hands free at all times.
Whenever President Barlett exits a limo, a secret service agent can be seen closing the door behind him. In actuality, the door is kept open to allow the president to re-enter quickly in case of an emergency.
Secret Service code names for the First Family always begin with the same letter (for example, the Obama family code names are Renegade, Renaissance, Radiance, and Rosebud), which means that if President Bartlet's code name was Eagle, Zoey's would not have been Bookbag. Her code name would have begun with the letter E as well.
In several episodes they reference Myanmar. In fact, the US along with most western governments do not recognise the name change and still call it Burma. Various Government sites including the CIA Factbook confirm this.
White House sugar packets do not have labels or manufacturers' names on them, only a presidential seal.
During outdoor scenes filmed for the 1999-2000 first season, the Washington Monument can be seen in the background encased in an elaborate blue mesh scaffolding used while the monument was undergoing a major renovation. However, in stock overhead shots used during the same episodes, the Washington Monument appears without the scaffolding (i.e., as it normally appears).
Some long shots of Washington from season 1 are flipped horizontally, e.g: at one point, the Smithsonian is north of the Mall.
In real life, Sam would have been fired and possibly prosecuted for his involvement with Laurie, the escort, long before they ceased contact with each other and definitely once the media got confirmation of their relationship.
Both Leo and Toby can be seen wearing wedding bands in seasons when their characters were divorced.
Several times characters refer to military hardware by incomplete names; for example: "AIM Sidewinder" missile instead of AIM-9 Sidewinder (as well as saying A-I-M rather than saying the word "aim"), "AH Apache" helicopter instead of AH-64 Apache.
Characters repeatedly refer to the lectern in the press briefing room as the podium. The podium is the raised platform on which the lectern and speakers stand.