I dunno about the set up on this one, isn't the point of murder mysteries supposed to be that there are clues sprinkled in so that it isn't completely out of nowhere?
Detective being focused on revenge toward a child killer due to guilt over his own daughter's death is random, and idol girl who Spica went to see suddenly being the murderer is also out of nowhere besides the "whistling" which only just got tied to her.
I'm also trying to figure out what Spica's "weakness" is, so far all I can think is that she's willing to commit murder herself so she's vulnerable to being caught if she's careless, but other than that there is no "downside" to her ability at all.
Edit: Looked through past chapters and still any clues are sparse. Only thing I'm seeing is that original Husband suspect might be listening to the Idol's music since the Fwee sounds coming from headphones are the same as what Idol is listening to/whistling. Other unresolved part is the "noise complaint" that someone downstairs from Husband suspect made which sent him into a rage. Maybe he's an otaku follower of Idol who was listening loudly to her music at home and always visits her at shows, and Idol actually loves him and wanted the family out of the way for him to focus on her?