Delaware was written to be deceptively antagonistic towards the protagonists, which was based on Mark Sheppard's past as villains for his work in American television.
The control room set used from The Lodger (2010) was used again for this episode. Steven Moffat wanted the set to be used again, feeling it would be a suitable Silence base. The set was adapted to give it a darker, evil feel. Because of this, fans have been theorising that the ship from "The Lodger" is the same ship here.
The Doctor tells Nixon that he has to tape everything that he says in his office or else he won't know if the Silence has affected him. This is a reference to the Nixon tapes, with the famous eighteen and a half minute gap in one of the tapes.
Incorporating Richard Nixon into the plot was accidental. Steven Moffat wanted to set the story during the moon landing and looked up the United States president during the time. He was initially disappointed that it was such a "rubbish one" and briefly considered using a generic, unnamed president, such as the one seen in The Sound of Drums (2007). However, he thought it "didn't feel right for a story partly about real events" and realized it could be fun to use Nixon. He believed there was something "comically awkward" about him, and it would be interesting for the Doctor to have to work with someone he did not like.
There were originally two running gags - the Doctor insisting on keeping his beard, and River refusing to remove his handcuffs. These eventually dovetailed when River advanced upon the restrained Doctor with a shaving razor in hand.