What is unusual about the point of view in "The Wrong Category" by Ruth Rendell?

Author Ruth Rendell was a master of writing mystery stories.  In her collection of short stories entitled A Fever Tree and Other Stories, she includes a story called "The Wrong Category." This story is interesting because the author seems to lead the reader right to the identity of the killer, only to completely change their mind right at the end.
Throughout the story, we follow Barry, an awkward, ugly little man who has taken to haunting the locations of several murders. His mother hates him going out at night to these spots, but he seems to enjoy visiting them. It would seem that we are reading the story through the perspective of the actual murderer!
Everything, it appears, would hint at Barry being the culprit of the murders; he fits the profile, he likes to visit (or revisit) the locations where the murders occurred, and he picks up a girl at the bar who fits the profile of the murdered girls.  In fact, he takes her to a location and suggests that this would be the perfect spot to commit another murder.  She runs, and he chases her.  
It would be obvious that Barry were the murderer, except for a few small details.  For example, was he simply trying to help her when she ran away from him at the murder spot? Why would he tell his victim and give her a chance to get away?  Perhaps he has simply realized something about the pattern of the criminal by taking up the hobby of following the murders.
As we can see, this unusual point of view is simply one ingenious device that the author uses to lead us in the wrong direction.  We only see what Barry is doing, so we naturally think everything he does is suspicious, which leads us to draw the conclusion that he must be the murderer.  The outcome of the story seems completely obvious.  We have a limited perspective, however, which leaves the author room to completely surprise us right at the end with some information that we never considered.  Rendell is a true master of mystery.