When "The Friend" says, "I stand flat-footed upon the ground... No ghosts need apply," this refers to what Sherlock Holmes said in the story "The Sussex Vampire", where a man consults Holmes because he fears his own wife may be a vampire, and Holmes endeavours to show that there is a natural explanation for the wife's behaviour.
Abercrombie Smith says to his friend Lee, "Treves has an opening at the Royal London." He is referring to the famous surgeon Sir Frederick Treves who in 1886 became associated with Joseph Merrick, the so-called "Elephant Man", and who in 1902 performed a successful operation on King Edward VII.