I think its Ray Haffner based on jane psychiatrists description . I think he didn't kill Teresa Lisbon because he is in love with her. The psychiatrists said that the person is a good whistler when Ray left Lisbon room he was whistling she also said he was narcissistic and Ray seem cocky when talking to Lisbon. I think the whole scared of height is a red herring i don't the person fear of height maybe fear of high objects or fear of flying hmmm.