The epistolary format was simply odd -- what detective would really send all the evidence home to his wife? Though it provided some slight human interest in terms of his home life, it mostly gave a distancing effect as conversations had to be reported by him instead of seen directly. I think the accompanying evidence (notes, news articles, reviews etc) could have been incorporated without making the whole thing a letter-writing exercise. Also, asking  the suspects to write letters instead of interviewing them seems far-fetched.

The musical murder was just too contrived to be convincing. It seemed the author came across this piece and thought "This would be a perfect spot to murder someone!" and then built a story around it.