Due to cable issues, I missed the second episode. Ironically, exactly why I lamented it being on PBS and not BBC America as with the latter I could at least watch it at a later date on the On Demand channel. No such luck with PBS, miss it and you're up the creek without a paddle.
The third episode concerns Mycroft's efforts to enlist Holmes and Watson in a case concerning the strange death of a government official and theft of government plans while a mad bomber straps bombs to innocent individuals and challenges Holmes to solve a variety of puzzles under different time limits (the accidental death of a swimmer years ago when Sherlock was a boy that he always suspected was murder, the apparent death and disappearance of a husband, the "accidental" death by tetanus infection of a television celebrity, and the death of a museum security guard). By the end, the identity of the bomber stands revealed as Moriarty and it ends on a cliffhanger.
With this episode, we get a major departure from the canon. There are several references to various Holmes stories, but it takes the characters and the show forward and let them develop a life of their own. "The Great Game" is a smart modern day thriller with powerful compelling characters inspired by Doyle's writing without being slavish to them. The story starts off referencing "A Scandal in Bohemia" which was the third story of Sherlock Holmes and thus the most likely subject for re-imaginings. However, it moves quickly from there to reference the stories "The Adventure of the Bruce-Partington Plans", "The Adventure of the Five Orange Pips", and the stand-off between the Great Detective and his arch-foe on the precipice of assured mutual destruction before a body of water is clearly from "The Final Problem". There's more humor at the expense of modern day sensibilities regarding Holmes' asexuality and the close friendship between two men and the two leads excel at capturing the essence of the characters yet presenting them as if new: a weary and worldly Watson who struggles with holding on to his optimism and humanity, especially in light of the other, Holmes never before depicted as being so truly cold and analytical and sociopathic yet somehow still passionate about his chosen profession in the service of others even though he cannot really relate to them. Watson's own humanity helps humanize Holmes.
I especially enjoyed the inclusion of a hulking hitman named Golem due to his size and strength and killing by strangling with his bare hands. He comes across as a gothic or pulpish throwback and the hunting him among the homeless beneath the streets briefly reflects a dark and shadowy world reminiscent of early German films along the likes of "Nosferatu" and "The Vampyre". Given the hitman's name, the association is more than likely intentional. Seemingly a minor and throwaway villain, he's exactly the type of minor character that is instantly larger than his small part and worthy of a fuller story built around him. Much as the legend and importance of Moriarty himself has become.
This third episode marks the end of the season, remarkably short even for one accustomed to the shorter English television seasons. I first became aware of this phenomenon watching "As Time Goes By" on PBS, and over time the characters aged rather dramatically due to two seasons being about the equal of one over here (and then the last several seasons skipped years).