I don't remember coming across as many new movies or television series about serial killers as, say, ten years ago. One such series was Dexter that had eight seasons between 2006 and 2013.
Here's an analysis by Dr. Todd Grande on how realistic Dexter's character is:
I'm no expert on the subject matter but I have to say that Dr. Grande's analysis aligns with what I felt was unrealistic about this relatable serial killer. In real life, these people do not have moral struggles or a philosophical approach, only grandiosity, narcisissm and frightening sadistic desires.
Here's an interview of a real world psychopathic serial killer before her execution.
This person does not make pleasant or even good television. It's hard to look at her in any kind of positive light.