The character of Greg Lestrade is a combination of Inspectors Gregson and Lestrade. In the books, the latter character's first name is said to begin with the letter G, but is never revealed. This is why Sherlock is always forgetting Lestrade's name.
Sherlock sometimes uses a memory technique that he calls a "Mind Palace." This is not an invention of the screenwriters; rather, it is a method of aiding memory that dates back to ancient Rome. One of history's most famous real-life practitioners was the sixteenth-century Italian Jesuit missionary Matteo Ricci, who introduced the method to China.
In this series, Watson was wounded in the shoulder but has psychosomatic/psychogenic pain in his leg. This is a sly reference to the original stories in which Arthur Conan Doyle was inconsistent about the location of Watson's war wound.
Through the series, several Holmes stories by Arthur Conan Doyle are alluded to, either as episode names or in passing. For instance, "A Study in Scarlet" becomes "A Study in Pink", "The Greek Interpreter" becomes "The Geek Interpreter" etc.
The role of Molly Hooper was never in the books or short stories and was only meant to be a one-off character to further indicate Sherlock's lack of social skills, particularly addressing any romantic encounters. However, Moffat and other producers loved Louise Brealey's performance so much that they decided to expand her character.
As in the Sir Arthur Conan Doyle stories, the term "deduction" is misused. Like medical diagnosticians, hunters and yes, detectives, what Holmes actually uses a form of inference called "abductive reasoning," which is neither deductive nor inductive.
In the summer of 2011 Danny Boyle created a National Theatre production of 'Frankenstein' in which Benedict Cumberbatch and Jonny Lee Miller played the creator and monster and alternately changed nightly. Both actors then went on to play another Victorian creation Sherlock Holmes, both set in the present day, allbeit opposite side of the Atlantic.
At one point in the series, Watson gets fed up with hearing Holmes talking about his intellect and how emotions are unimportant to the point that he sarcastically calls Holmes "Spock". Benedict Cumberbatch appeared in the Star Trek film "Star Trek: Into Darkness" as Kirk and Spock's arch-nemesis, Khan.
In this new series Dr. Watson used to be a Captain (and medical doctor) serving with the 5th Northumberland Fusiliers deployed to Afghanistan. The 5th Northumberland Fusiliers did indeed serve in Afghanistan in the Second Afghan-Anglo war (1878-1880). The first story of the old Sherlock Holmes series took place in 1881. The 5th Northumberland Fusiliers, however, was renamed into the "The Northumberland Fusiliers" in the year 1881 (no 5th left in title), which means the modern Dr. Watson service with the 5th Northumberlands is a nod to its old heritage. The former 5th Northumberlands evolved into its last formation named "Royal Northumberland Fusiliers" and was deactivated in 1968.
Watson's reference to Holmes as "Spock" has another significance. The original Spock, Leonard Nimoy, has also played Sherlock Holmes. Nimoy also recorded a song called "The Ballad of Bilbo Baggins," based on The Hobbit. Martin Freeman and Benedict Cumberbatch appeared together in the film adaptations.