The nuclear test depicted is similar to a nuclear test conducted in 1979 by an unknown nation. To this day, the country that conducted the test is not known, but Israel is one of the suspects.
Josh (Bradley Whitford) discusses the tragic life of Blind Willie Johnson and his inclusion on the Voyager Golden Record. It is not certain that he was blinded with lye by his stepmother, but that is one theory - biographical details are sketchy.
The NASA officials talk to Josh (Bradley Whitford) about needing to launch soon to take advantage of a gravitational slingshot at Jupiter for the purpose of exploring the Kuiper belt. While not named, the real-life New Horizons mission was facing administration opposition at the time, and likewise had a 2006 launch window to be able to use Jupiter's alignment to reach Pluto and the Kuiper belt. Fitting the theme of this subplot, the New Horizons encounter with Pluto in July 2015 garnered significant positive publicity for NASA, including display of Pluto images in Times Square.
The main plot of this episode closely resembles the Vela Incident, although in the real-life incident the responsible party was never found, nor was it ever confirmed there actually was a detonation.
The Mars Direct described by Alex Moreau (Christina Chang) is a real-life concept for crewed Mars exploration.