The baseball cap on the display case behind Sam Seaborn's desk changes from one bearing the Alcohol, Tobacco and Firearms Agency (ATF) logo to one bearing the Drug Enforcement Agency (DEA) logo between Mallory storming out to confront her father and returning later to ask Sam out for coffee and dessert.
President Bartlet says, "Shenandoah National Park, right here in Virginia." The president is in the White House, in the District of Columbia.
When the vice-president comes into the oval office, the president is annotating a report; he appears to write something in the margin but when the camera turns, the paper has no annotations on.