It was a fun mystery/drama that managed to be rather light hearted despite its darker subject matter. Moriarty is a kind of Robin Hood character except instead of stealing from the rich and giving to the poor, he helps the poor murder the rich; often in ever more increasingly elaborate ways.
It tries to tackle some interesting moral questions, but in my opinion doesn't delve very deep into them and thus is kind of shallow. "Rich people are terrible, the world would be better without them, so to bring about that better world let's kill them". Additionally, each "villain" is comically villainous to the point of seeming to lack any humanity or redeeming qualities, thus making it easy for the audience to sympathize with Moriarty's views without question. Holmes is the only one we really get to see grappling with the morality around killing someone, but even that isn't given much serious attention.
Additionally I felt some of the more "anime-esque" additions kind of took away from the "real world" settings they were placed in. i.e. characters leaping onto and off of multi-story buildings, some of the hand to hand combat techniques, wearing cloaks whenever engaging in shady business, etc.
Overall it was an enjoyable watch, nice to look at, rocking music for both the opening and ending, and had interesting enough stories to keep my attention, but it could have done more with its premise and wasn't spectacular, thought provoking, or particularly memorable.