"The man with the blue coat and the roll of paper is Sir William Baskerville, who was Chairman of Committees of the House of Commons under Pitt."
Chairman of Committees is the presiding member of the House of Commons. William Pitt (1759-1806) was Prime Minister of England from 1783 to his death in 1806. He presided over the British government during one of its most tumultuous periods, including the aftermath of the American Revolution and the rise of Napoleon. Conan Doyle places Sir William Baskerville, an entirely fictional character, at a crucial moment in British history.

	A portrait of William Pitt from Earl Stanhope, Life of the Right Honorable William Pitt, vol. I, 1861

"And this Cavalier opposite to me—the one with the black velvet and the lace?"
During the English Civil War (1642-1651), the royalists called themselves "Cavaliers." The Cavaliers tended to dress more flamboyantly and wear their hair longer than their Puritan opponents, contemptuously known as "Roundheads" for their close-cropped hair.

"Yes, it is an interesting instance of a throwback, which appears to be both physical and spiritual. A study of family portraits is enough to convert a man to the doctrine of reincarnation. The fellow is a Baskerville—that is evident."
Although we were earlier led to suspect that the hound itself might be a throwback, now it becomes clear that Stapleton is the throwback, reproducing the ruthless and cruel personality of Hugo Baskerville, as well as his physical appearance. Why Dr. Mortimer, an expert on atavism and a frequent visitor to Baskerville Hall, did not notice the resemblance is difficult to say.

He burst into one of his rare fits of laughter as he turned away from the picture. I have not heard him laugh often, and it has always boded ill to somebody.
Sherlockian Christopher Morley (1890-1957) says this of The Hound of the Baskervilles:

Probably the masterpiece. There are moments of anxiety and shock which no story in this vein has improved. From the moment when Holmes, looking at Mrs. Hudson's well-polished silver coffeepot, sees the image of Watson studying the "Penang lawyer" (a walking stick) the reader is carried in an absorption we would not spoil by giving any hints. Holmes rarely laughed, and when he did so it boded ill for evildoers. Toward the end of this superb tale we hear his strident and dangerous mirth.

—From Sherlock Holmes and Dr. Watson: A Textbook of Friendship (1944)