The DVDs that the Doctor says are in the bookcase that will bring the TARDIS to him, is a reference to Blink (2007). They are the 17 DVDs that he made for Sally Sparrow to take the TARDIS back to him in 1969.
Peter Capaldi confirmed that he wore David Tennant's spacesuit from The Impossible Planet (2006)/The Satan Pit (2006) and The Waters of Mars (2009).
The filming location for the moon was Lanzarote, which 30 years earlier was the filming location of "Planet of Fire". The production team played upon this - early drafts of the script were titled Return to Sarn just to mislead those who theorised that this story would feature the return of the Master.
During the writing process, Steven Moffat told Peter Harness to "Hinchcliffe the s**t out of it", in particular the first half. This referred to the period when Philip Hinchcliffe was series producer (1975-77), which is remembered many as especially frightening.
Not the first time the Doctor has encountered spider-like creatures. In Jon Pertwee's final story "Planet of the Spiders" in 1973, the Third Doctor and Sarah Jane Smith discovered mutants spiders had gripped a colony on the planet Metebelis 3 in the far future, in a grip of future.