Although it is well established that Toby (Richard Schiff) is no longer married, he can clearly be seen wearing a wedding band. (Richard Schiff said he purposely wore a wedding band even though Toby was divorced. This was his way of showing that the character wasn't ready to accept being divorced.)
The last Congressman on Leo McGarry's list at the outdoor restaurant is "Sugarbaker", a reference to Suzanne Sugarbaker of "Designing Women" and its spin-off "Women of the House" where the character was elected to Congress.
C.J. (Allison Janney) was actually correct to say that the President was under no legal obligation to appoint a Democrat and a Republican. Though 2 U.S.C. § 437c(a)(1)-which has since been editorially reclassified as §30106 of Title 52, Voting and Elections-does state that no more than three members of the FEC may be affiliated with the same political party, it does not require that all the members be either Republicans or Democrats. President Bartlet could have legally appointed someone affiliated with a third party to either or both of the open seats.
Leo (John Spencer) holds a breakfast meeting with senior staff at the Iron Gate Inn, as seen on the menus used in the scene. Although there is no "Iron Gate Inn" in Washington, DC, there is an Iron Gate restaurant on N St NW, which has an outdoor patio similar to the fictional restaurant used in the scene. Directly across the street from the real Iron Gate restaurant is the Tabard Inn, which also features a visually similar outdoor patio eating area. It is very likely that the producers came up with the "Iron Gate Inn" name by merging these two restaurant names.
The episode opens with the President giving a speech at the "Sheraton Centre Hotel" in Washington DC but there is no such hotel.