The episode features news coverage of President Ronald Reagan's "We begin bombing in five minutes" gaffe. So, the episode occurs on or around August 11, 1984.
Viewer sympathy for Martha led to the popular feeling that she should be able to return to the U.S. While this would be possible, the statue of limitations for cases of espionage is ten years, which means (barring complications and legal maneuvers by Federal prosecutors) that she would not be able to return until late 1994 at the earliest.
Elizabeth is reading the book, "Space: A Novel" by James A. Michener; a history of the space program told using fictional characters.
Both Keri Russell and Irina Dvorovenko ("Evgheniya Morozov") are trained dancers. Irina was a lead dancer with the American Ballet Theater. Not being a strong singer, Keri's dancing skills were key to her joining the cast of The All New Mickey Mouse Club (1989).
The poster visible in Pasha's room portrays Alla Borisnova Pugacheva, Alla Pugacheva, a worldwide fame musical performer even back in USSR-era days.