The title is a loose reference to "The Hound of the Baskervilles", probably the most famous of the four Sherlock Holmes novels. A later episode, Hounded (2016), takes up the Baskerville story line.
Watson comments on the suicide by Helium, "The body doesn't even know it receives no oxygen and you just go to sleep." While true, technically, what the body fails to realize is that it is not producing any carbon dioxide. The build-up of excessive carbon dioxide in the blood is what triggers the strong breathing impulse when simply holding one's breath or suffocating in a plastic bag.
The victim's voice rises in pitch when they are breathing helium. This is correct, and often done as a party trick with the contents of a helium balloon. It is due to the gas's lower density.