Unlike most episodes of the series, the main plot of this episode was a dramatic invention: no evidence exists that the real Prince Philip was fixated on the moon landing. According to royal historian Sally Bedell Smith, "The idea that he was obsessed with them and had a midlife crisis over not being on the Moon is really preposterous".
The astronauts are portrayed as rather unsophisticated rubes. While this serves the purposes of the plot, it is a disservice to the men. All three were educated men who had already traveled widely as a result of their prior spaceflights. Armstrong was known to do research on the countries the crew visited in order to develop a rapport with the leaders they met. Aldrin and Collins were both West Point graduates, where they learned poise and leadership. Collins was the son, nephew, and brother of Army generals, became an Air Force general himself, and went to work at the US State Department after leaving the space program. At this point in their lives these men would have been more than capable of conversing with royalty with the dignity and grace required of the situation.
Claire Foy, who played Queen Elizabeth II in the first two seasons of The Crown, also played Janet Armstrong in First Man (2018).
The astronauts who landed on the moon were all depicted as short, while in reality Neil Armstrong for instance is 6 feet tall.
Tim McMullan, who portrays Robin Woods, also portrayed Stephen Lamport, Private Secretary to the Prince of Wales, in The Queen (2006) and King Charles III's press adviser in King Charles III (2017).