I read this description, and had an instant thought of a possible title. I mention this title with a full admission that I have never seen this film, but the description kind of fits.
"Eyes Of A Stranger" http://www.imdb.com/title/tt0082352/
Lauren Tewes plays a reporter, and the killer taunts folks over the phone. It also fits the time frame that the original poster would have seen the film.
Just a suggestion.