Actor William Gillette playing Holmes, wearing a dressing gown and thinking through a problem while smoking his pipe, from "Mr. William Gillette as Sherlock Holmes," The Strand Magazine, Vol. xxii, December 1901
	In "The Man with the Twisted Lip," Holmes stays up all night thinking over a problem

"…one a farrier…."
A farrier shoes horses, as opposed to a blacksmith, who forges metal items such as horseshoes. "Farrier" and "blacksmith" are often used interchangeably. The doctor's point is that the three people who claim to have seen the hound are levelheaded country folk, not normally given to flights of fancy.

"And you, a trained man of science, believe it to be supernatural?"
A doctor and a "trained man of science" like Mortimer, Conan Doyle had no trouble believing in the supernatural. He attended s?ances and believed in fairies.

"…who arrives at Waterloo Station…."
Opened in 1848 and rebuilt several times since, Waterloo Station serves the south and southwest rail corridor from London. It is located in Lambeth, across the Waterloo Bridge and about three miles from Baker Street.

"…fled to Central America, and died there in 1876 of yellow fever."
Found in Africa and South America, yellow fever is a viral infection transmitted by mosquitoes.

"I have had a wire that he arrived at Southampton this morning."
Southampton, located on the south coast of England, is a major port.

"…with merely local powers like a parish vestry…."
That is, a local parish council.

"When you pass Bradley's, would you ask him to send up a pound of the strongest shag tobacco? Thank you. It would be as well if you could make it convenient not to return before evening."
When Holmes has a problem to think through, he prefers to smoke shag tobacco, a coarse, cheap tobacco with a high nicotine content favored by workingmen.

"I therefore spent the day at my club…."
The gentleman's club was a refuge away from home for the middle- and upper-class man, and lasted as a widespread institution well into the 20^th century. Club membership was very exclusive, and was predicated on social standing, military service, interest in cricket, hunting, etc.