With the story, I have a couple of issues. I solved a major clue at the beginning as soon as it appeared. One of the great delights of reading Holmes is seeing his deductive power in action. Even when he is puzzled, you can count on him having worked out more than anyone else. For the reader to be ahead of the detective is surely a fundamental flaw. I also thought the final revelation was not only obvious (did anyone seriously not know what was coming halfway through?) but sensationalist which was disappointing.
The style and the language were quite well mimicked although some modern sensibilities did leak in. The observations on poverty etc. were out of place as was Holmes' internal reflection and guilt - like Watson was apologising for not being conscious of these things before. It was unnecessary and only served to remind you that this isn't a 'real' Holmes story.
I also picked up on some grammatical errors like the use of 'infer' as opposed to 'allude'; something that Doyle never got wrong.
Despite all of that, I can't deny that this was a page turner and whatever my thoughts on its success or failure specifically as a Sherlock Holmes novel, I got through it pretty fast. As entertainment, it did the job; as an addition to the original set, it missed the mark for me and I imagine it will for any hardcore fans.
When I read this a while ago, I got the impression it was set up as a one-off but I notice the title now includes 'Novel 1' which presumably means Horowitz will be writing more. It won't be at the top of my reading list...