The murder of Ronald Adair is the case Holmes is investigating when he reappears after his apparent death in the original stories.
The song that starts as Sherlock is at the cemetery (The Optimist by Zoë Keating) is the same song that plays as Sherlock introduces himself to Joan in the pilot episode.
During his 3-year hiatus after his apparent death in the original stories, Holmes goes to Tibet and uses the identity of a Norwegian named Sigerson. Sigerson was also the name of Sherlock's fictional younger brother in the Gene Wilder comedy The Adventure of Sherlock Holmes' Smarter Brother (1975).
The epithet on Sherlock's headstone states "Work is the best antidote to sorrow".