Conan-Doyle's wife did die from tuberculosis in 1906.
The episode name "Belly Speaker" is a literal translation of the word "ventriloquist", which comes from the Latin words "ventrum" (stomach) and "loquor" (I speak).
The ventriloquist's dummy is called Mycroft, the same name that Sir Arthur Conan Doyle (who appears in this episode) gave to Sherlock Holmes' elder brother.
When Harcourt Grimesby is being interviewed by Detective Murdoch, he states that, 'you don't leave your best friend alone in the dead of night.' Dead of Night is a 1945 British film which is a montage of short stories. One of the stories featured a ventriloquist whose dummy appeared to have a life of its own, similar to 'Mycroft' in this episode.
Murdoch refers to a recent case that has been solved a a 'cold case,' exactly the opposite from the definition that is currently popular.