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The Doctor claims that he himself planned to use a box with a button to commit mass murder. This is a reference to The Day of the Doctor (2013) when three of the Doctor's past incarnations planned to use the Moment, a Time Lord doomsday device, to end the Time War.
Kate describes how she escaped from a Zygon by saying "Five rounds, rapid." This phrase was first used by her (Doctor Who-universe) father, The Brigadier, in The Dæmons: Episode Five (1971) and the name of the actor's memoir: "Five Rounds Rapid! The Autobiography of Nicholas Courtney - Doctor Who's Brigadier."
The helmet which Ashildr used to defeat the Mire is stored in the Black Archive.
Osgood has now worn the 12th Doctor's sonic sunglasses, continuing her tradition of wearing items from the various Doctors.
According to Peter Harness, the Doctor's de-escalation speech originally included several additional sections. These were cut out of the final draft of the script, mostly for pacing reasons. One of the sections included the Doctor asking Bonnie about whether everyone will be forced to grow and eat beetroot. During a convention appearance in New Zealand a few weeks after the episode aired, Peter Capaldi performed a version of the complete speech.
UNIT's Black Archive, first seen in The Day of the Doctor (2013) and containing items from several past episodes, currently has a Mire battle helmet first seen in The Girl Who Died (2015).