Arachnophobia is the most common phobia in European societies (including areas settled by Europeans in the Americas and Australia).
This episode takes place in 1901.
The names of the exhibited by Dr. Ogden's patients include arachnophobia (spiders), equinophobia (horses), and an extreme case of stage fright (performance anxiety). While there is no name for fear of feathers per se, the fear of being tickled by feathers is pteronophobia. Murdoch's fear of butterflies is called lepidopterophobia.