The case involving a mongoose that Sherlock describes to his addiction group is Arthur Conan Doyle's Sherlock Holmes short story "The Adventure Of The Crooked Man".
Holmes claims to be able to identify 140 different brands of cigarettes and cigars by their ash alone, which he says Watson would know if she read his monographs. This is a reference to the original novels, where this is used to show the methodical and focused nature of Sherlock Holmes.
The porcelain bust, named Angus, is a replica of the L. N. Fowler phrenology bust circa 1840. The Fowler brothers published books on the subject and made these busts as study aids. While that pseudoscience held some repute at that time, the old school phrenologists of Europe regarded the Fowler's approach as vulgarly misguided. Nevertheless, possessing one of these busts has long been a sort of in-thing for scholarly folks.
Rhys says he's not a wreck because "I believe in Sherlock Holmes." That particular slogan was popular on the internet around this time in relation to the series two finale of the other modern day Sherlock Holmes, Sherlock, and even eventually made it into the series three premiere when the show later returned. Series two had ended in "The Reichenbach Fall" (loosely inspired by "The Final Problem" of the original stories) which saw the main character presumed dead and widely hailed as a fraud who committed crimes so that he could look clever solving them; the slogan was used both to indicate belief in him as a genuine detective and good man and belief that he would return (as he had in the original stories and as it was suggested he would at the very end of the episode).
The abductor demanded 2.2 million dollars for the Emily's release. He sent a severed finger. Sherlock Holmes says that he got a loan of 2.2 millions from his dad to give to the kidnapper. This resembles a real episode when the oil tycoon John Paul Getty III's grandson was abducted, the kidnappers sent the boy's severed ear to the family. The ransom demand was 3 million dollars. The oil baron loaned 2.2 million dollars ( on interest) to his son for the release of his grandson.