The Special Operations Executive (SOE) that Peggy is seen being recruited for was a real organization run by the British during World War 2. Nicknamed the Ministry of Ungentlemanly Warfare and Churchill's Secret Army it combined intelligence and fledgling special forces to infiltrate behind German lines in Europe and conduct espionage, assassinations and sabotage as well as training native resistance groups. Unusual for the era, and as shown here, they did use women as field agents as they would arouse less suspicion than many male agents would.
A lot of thought was put into the creation of Peggy's wedding dress seen during a flashback to 1940 by costume designer Giovanna Ottobre-Melton. In 1940 new dresses were a luxury, so instead of silk, the body was made out of the less expensive crepe. The trim consists of two different types of lace, implying that Peggy's mom used parts from her own wedding dress as well as her grandmother's Victorian -era dress, as lace was in short supply.
Bletchley Park in England is where German codes were deciphered and the place where the German enigma code was cracked by a team that included Smoke & Mirrors (2016). Codebreakers were mostly recruited from the top academic and civil service posts, mostly by word of mouth.
Jarvis mentions that Hedy Lamarr is about to divorce her third husband. The character of actress/scientist Whitney Frost is loosely based on Lamarr, an actress who held a patent for a frequency-hopping guidance system for torpedoes. Patented around the time of World War II, the technique was put into use by the US military in the 1960s and variations on this principle remain a critical component of wireless communications.