In one of the television news broadcasts, Bartlet is referred to as 'former Governor' of New Hampshire. In later episodes, Bartlet was still in office as governor while receiving briefings after winning the election.
When Secret Service Agent Ron Butterfield realizes that the President had been shot, he yells at the limo driver to take them to the George Washington University Hospital instead of the White House. The limo driver does a u-turn on a bridge. GW is a mile west of the White House, and the nearest bridge is west of the hospital. The limo driver is going the wrong way despite the driver's presumed knowledge of D.C. streets.
As Sam is trying to persuade folks to listen to his idea to improve the ship purchase deal, he used the phrase "bear me out" when he seems to have meant either "hear me out" or "bear with me." It's unclear whether the mistake was I. Aaron Sorkin's script or Rob Lowe's delivery.
In the scene in the Bartlet campaign headquarters in Manchester, New Hampshire, the camera pans across the room and there is a bumper sticker on the side of a PC monitor saying "Bartlet / Hoynes". This scene is set during the primaries where Bartlet and Hoynes are still competing for the Democratic Party nomination, and Hoynes would not yet be the running mate.
In a flashback, Josh is seen attempting to call Sam using a Verizon telephone booth. It can be assumed that this flashback occurs somewhere between 1996-1998, as it takes place shortly before the 1998 presidential election. Bell Atlantic did not change their company name to Verizon until June 2000.
In the penultimate scene where Bartlet is shaking hands as he walks down the terminal concourse, the camera crane is reflected in the chrome panels of the wall in the top of the shot.
One of the crises in "In the Shadow of Two Gunmen" is the question of who is in command while President Bartlet is under general anesthesia. Several characters say that, under the 25th Amendment, the only circumstances in which the Vice-President can take charge is if the President is dead or if he signs a letter declaring himself incapacitated. This is not true. Under the same Amendment, the Vice-President and a majority of the Cabinet can declare the President incapacitated, transferring power to the Vice-President. (That provision exists specifically for situations like this.) However, a deleted scene between Danny Concannon and Leo McGarry clears this up later. Danny and Leo agree that they "did not want to invoke the 25th", meaning that they preferred to not go through the necessary measures to remove the president from power for the three hours that he was under anesthesia. This deleted scene can be found amongst the extras included on the DVDs of the second season.
Josh says that his father's pulmonary embolism went to his heart. By definition, a pulmonary embolism goes to a lung (after traveling harmlessly through the heart).
During one of the press briefing scenes CJ tells the press that the two gunmen were shot using 7.26mm calibre rifles. This should be 7.62mm.