When Rose first arrives at the Martin household, there is a shot of her standing in front of the house with light shining down on her from a window. This is a recreation of the poster image from The Exorcist. There are several addition nods to that film, including an overt one when Martin mentions it by name.
According to the cast, neither Maeve Higgins (Rose) or Claudia O'Doherty (Claudia) can drive in real life. Ironically, both Will Forte and Barry Ward, whose characters both take driving lessons in the film, can.
The first time Martin expels ectoplasm, Rose collects it in a "McGuffin's" brand candle jar. In fiction, a MacGuffin is an object that is necessary to the plot and the motivation of the characters, but insignificant or unimportant in itself.
Christian Winter was influenced by a raft of celebrities who moved to Ireland in the 80s and 90s to avoid tax.
The phone number for the driving school is 0855378008 - on the old upside down calculator trick this spells "boobless bo"