Bartlett stopping to tie his shoe was improvised by Martin Sheen.
The title implies that this is President Bartlet (Martin Sheen)'s third Sate of the Union. States of the Union are given every year except the first year in office. So while this might be the third year in office, this would have been the second State of the Union.
Normally the President of the United States is ushered into the House chamber by a group of Congressmen and Senators. In the show - Bartlet (Martin Sheen) arrives at the door of the House chamber unescorted except for Presidential staff.
According to the news announcer at the beginning of the episode: Edgar Finney is the Doorkeeper of the House. The office of Doorkeeper was abolished in 1995 during the 104th Congress.
Mickey Troop (Tony Plana), who advises the President on the Colombia crisis, is the Secretary of State.