If you've forgotten, the key plot twist is that only the kid can see Crowe's ghost -- Crowe talks to Cole and no one else. Which means that one thing Crowe, genius child psychologist and literal child savior, doesn't do in his ardent mission to help this poor kid is talk to the kid's mother. Or teachers. Or anyone else that an actual child psychologist would be interested in talking to in order to gain some much-needed context and perspective on his patient.
Although after the Munchausen-by-proxy mom, can you really blame him?
Now, the movie excuses Crowe's lack of interaction with the world in general because he's deluded about the fact that he's dead -- his wife doesn't speak to him, but he assumes it's because their marriage has grown cold and distant. He doesn't have any friends because he has withdrawn from society since the shooting. But how in the hell could he think he was doing an awesome job at child psychology without talking to the people in the kid's life?
Because this is key information he's missing here -- did he not think Cole's mother might have something to say about the clearly visible injuries running up and down her child's arms? This means Crowe is apparently getting his entire case history exclusively from Cole, a kid whom he believes to be delusional. And it's not like a bunch of events conspire to prevent these conversations, either -- he's in the same room as Cole's mother several times, and instead of talking to her, he apparently just ... quietly stares at her.
Words won't tell you half as much about a person as a long, silent stare.
For example, eventually Cole gets hospitalized, and when the doctors in the ER see all of his cuts and bruises, they suspect Cole's mother might be abusive. They bring a social worker in to ask her some questions. As this is happening, Crowe is sitting right there, visibly disagreeing with what the ER doctor is saying. But rather than sharing his expert opinion and making sure Cole's mother doesn't go to jail, he just sits there. Does Crowe not understand that the mother is the one good thing in Cole's shitty life full of bullies and poltergeists? Why does it never occur to him to do anything but shun her?
"Note to self: I should probably get around to exonerating Cole's mom sometime."