One of the pictures that Bill sees while she is reviewing the history of Earth on the spaceship is a self portrait of Vincent van Gogh. It's the same portrait that Vincent offered the Eleventh Doctor as a parting gift in Vincent and the Doctor (2010). This portrait is not a true replica, but rather it's slightly altered to resemble Tony Curran, who played Vincent.
Keen to draw upon genuine scientific notions in his work, Frank Cottrell Boyce had developed relationships with various academics including Tim O'Brien, an astrophysicist at the University of Manchester. He suggested that much of the initial work of establishing a human colony on another planet would probably be performed by robots; indeed, this had been the idea behind the Mechonoids in The Planet of Decision (1965).
The story was set in a virtually empty colony world in order to permit the emerging relationship between the Doctor and Bill to remain a principal focus of the story.
The Doctor says "I'm happy, hope you're happy too." This is also a line from David Bowie's 'Ashes to Ashes'. Peter Capaldi is a big Bowie fan.
The planet to which humanity had come was originally called Gliese 581 D, but Frank Cottrell Boyce had previously dubbed it Erehwon, which instead became the name of the colony ship. It was derived from Samuel Butler's satirical 1872 novel Erewhon, or Over The Range which was set in a newly-discovered country called Erewhon, an anagram of "Nowhere".