I liked it mainly because I find the trope it mocks to extremely obnoxious. I hate these impossibly astute observational skills and the stupid closeups that go with them. Really I hate pretty much all crime shows.
I watch so many crime shows, and I was going to say that Sherlocke is definitely the worst for this. He's basically magic. But there was an episode of CSI Miami where they enhanced a photo of a person holding a plane ticket to scan the barcode on the plane ticket and find their flight, and Lie to Me was. basically about a psychic being taken seriously. What I'm saying is, I have terrible taste in mindless, procedural television shows.
It's represented as induction in the show/books (deduction deals with logically necessary consequences, induction deals with probabilities), but what he's actually doing is probably closer to abductive reasoning (we can infer A from B if A is a plausible explanation of B).
I saw one episode of Sherlock, and I dunno if I like all the reliance on smartphones and such. It'd be hard to make it modern without all that stuff, but still. I wonder if we're thinking of the same joke: basically Sherlock is out of work because someone with a computer just does it a lot faster.. something like that..