The ability to yield to a question without ending a filibuster was an important plot point in the classic film Mr. Smith Goes to Washington.
The "Dear Dad" concept of narrating the story through the point of view of the characters writing mail to their fathers was made popular in the TV show M*A*S*H. Alan Alda, whose character Hawkeye writes a letter to his father describing what a doctor's life is like in the Korean War in multiple episodes of M*A*S*H, also starred in later episodes of the West Wing.
When recounting the story about being yelled at by an intern from the GAO, Sam (Rob Lowe) calls it the General Accounting Office. The entity is now known as the Government Accountability Office, with that change occurring in 2004 - some three years after the original air date of this episode.
Towards the beginning of the episode CJ says to the press core about the ongoing filibuster that they are 'looking at democracy at work and it is a beautiful thing'. This is an exact quote that Elliot Hirsch gives on the third episode of the Newsroom, 11 years later, the 112th Congress in regards to voting in the election highlighted in that particular episodes. The link being both shows and episodes written by Aaron Sorkin.
The flag hanging behind senator Stackhouse is the Norwegian flag, as first flown in 1899, six years before Norway gained its independence from Sweden.