Inevitably I started by comparing with the Moffat "A Study in Pink". Common elements obviously include Watson's time in Afghanistan and the cab driver, and I had forgotten about the bit with the pills being also in the original. The TV version is less satisfying as a mystery; in the original, Holmes works out who the murderer must be pretty early on by powers of observation and deduction, and then uses unorthodox methods (the Baker Street Irregular) to track the killer down. Much of this happens off-screen, in Holmes' head, but it works in the voice of the baffled Watson. The Mormon back-story is merely chrome - any old grudge would do for plot purposes, though the TV version skipped even that - but gives Doyle a chance for imaginative and descriptive writing.
One point that struck me more forcefully this time round is Doyle's merciless portrayal of police manipulation of the media to show themselves in the best possible light. In a story which is full of trendy commentary - Holmes is at the cutting edge of biochemical technology, he goes to see the current star female musician - this reads to me like a tremendously subversive and very direct attack on the integrity of the state institutions of coercive force, and their successful formation and constraint of public opinion. Perhaps this seemed normal enough to me as a teenager growing up in Belfast, but it feels rather shocking to me now for a writer of the 1880s to say this. It furnishes Holmes with the sardonic Latin epigram which ends the story. Of course it's partly to reinforce the image of Holmes as background genius, but I think there is a sincere political commentary there too.
(And finally, I am always amused by my brother's appearance in Chapter 5.)