Senator Vinick's shoes being shined are from Allen Edmonds, famous for their handmade shoes of every US President since Ronald Reagan.
In one of their most thoughtful and politically charged tricks, Penn and Teller (Penn Jillette) make a U.S. flag seem to disappear by wrapping it in a copy of the United States Bill of Rights, and apparently setting the flag on fire, so that "the flag is gone but the Bill of Rights remains." In the episode, the flag remains missing, unlike in the stage version. Penn is quick to point out that, as seen in their stage show, the flag-burning routine "is astonishingly patriotic." It includes his observations about the greatness of being able to perform such a trick in a free country, proceeding to do the same trick but with the "Chinese Bill of Rights" - a sheet of cellophane - and turning around to show what happens to the flag, and finally, the flag not only reappears unscathed, but "up on the flag pole where it started, waving in the breeze."
The title comes from the question that many people were asking: Was the President (Martin Sheen) in the room at the time of the flag incident.
This episode is about a flag burning at Zoey Bartlett's birthday party but according to everything Wikipedia, The West Wing fandom her birthday is February 20th. this episode was aired on December 8th