Gripes:
Scheme: Again, Spica could easily have been killed anytime during this "she got caught" phase. The criminals intended to kill her, all they had to do was shoot her. Or maybe they never took off her gag allowing her talk, and then killed her. ... Oh wait...
So grandma is listening in to the whole thing over the phone, and then sends in "inaba" messages as needed to interupt if they got close to killing Spica. Okay, that would help.
Inaba Reveal: I would have to go back and re-read the entire thing to figure this out.
Side Character Catch-up Genius: I hate this trope where the author wants some side character to catch up on what's going on, so the side character suddenly starts jumping to (perfectly accurate) conclusions based on very insufficient evidence.
False Arrest: In other words, he arrested the wrong guy. And... the police failed to browbeat him into a confession for a crime he didn't do. And/or the real criminal came forward, or otherwise they failed to convict.
Japan's conviction rate: Over 99%. See
Japan Crime: Why do innocent people confess. So this guy's superiors punished him because the person he arrested managed to not be convicted.
Breaking out of chair: I'm assuming that it was something weak like a strip of fabric and she wore it down while they weren't looking. But that's some pretty incompetent criminal action.
Grandma/Spica Relationship:
They're not blood related, so no inheritance of psychic abilities. (Probably. With Japan you never know when hidden incest will pop out.) Oops, I misread the story, and somehow thought that Spica was a stepdaughter (or step-grandaugther). But no, she's a normal blood relationship.
Spica Head Trauma: Possibly head trauma is excuse/reason for her sociopathy and/or psychic abilities. (Extra points if it's "Grandma summoned a spirit/demon to possess her step-granddaughter's comatose body.")