Not really a plot hole. You see, the Doctor, after Walter ended up in his facility after his attempt at suicide, stated that Walter suffered from survivor's guilt with a combination of a numerology obsession, the book being a manifestation of Walter's insanity and grief and coming out as a work of fiction instead of a truth. It is possible that the police may have considered Walter as a suspect but took the Doctor's word on it, taking into account that he had been in that room for days and the news had released the story about the murder (basically, they may have thought that Walter, being completely nuts, saw the murder report on the news or read it in a newspaper, and incorporated into his twisted fantasy after the Doctor points this out, so they end up ruling him out as a suspect).
Not only that, if you look at the scene where you see him writing on the walls, there are sections where the text has been written over multiple times to the point where you can't decipher what is written. So, even if the police did read the chapter written on the wall, they'd either believe it was a false confession from a nutjob who happen to hear about the murder on the news or they could only read bits and pieces and the rest of it was overwritten so many times they couldn't figure out what was being said. And before you say, "But Walter is reading it in the film," keep in mind that not all of what you're hearing is the writing on the wall. Walter only written a little bit and then jumped out the window, to which he lost his memory after that. Walter couldn't have come back to the room and write about his time in recovery, meeting Agatha and the number obsession transferring over to the Doctor. All that we hear and see in that scene is the memories resurfacing and Walter, who has been acting as our narrator, been telling the audience the whole story after the events seen.
But this one's eating my popcorn!
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