I know the whole idea is that the dead see what they want to see, but...
In the scene where Cole comes home from school and Crowe is sitting in a chair in the living room opposite Cole's mother, wouldn't Crowe have found it odd that there was no conversation or acknowledgement of his presence by the mother? It's not often one visits a stranger's home and there is no interaction whatsoever between guest and homeowner.
I almost felt that this was a slight flaw in the story..Crowe never even says anything to the effect of "Why doesn't your mom talk to me? Does she dislike me or something?" As a psychologist who understands normal human behavior, I would think he at least would find that situation at least questionable. I know it was done to throw the audience off, but it doesn't make much sense. It would almost certainly be an obvious clue to Crowe that something was not right.
"Now, tart face, take your Clark bars and get outta my house!!!"