Jonathan Frakes previously directed Star Trek: First Contact (1996), which likewise explored the aftermath of World War III.
The door chime to Captain Pike's ready room is the same as from Star Trek: Voyager.
This episode takes place 3 years after the events of the pilot: The Cage (1966) and 10 years before the events of The Menagerie: Part I (1966) (and Pt. 2).
Marina Sirtis, who played the character of Counselor Deanna Troi on Star Trek: The Next Generation (1987), showed up on the set, having been invited by director Jonathan Frakes.
Ensign Tilly went to "Musk Junior High". While it could be named for someone who comes along in the next 200 years, Elon Musk is probably a good guess for the school's namesake.