If you are writing to someone who has a doctorate or medical degree, use the abbreviated form: "Dr." However, for other titles, such as professor, judge, rabbi, etc., write out the full title and capitalize it. For example, your salutation in a letter to a judge would be, "Dear Judge Barnard." Or, if your correspondence was with a rabbi, you might write, "Dear Rabbi Williams."
When writing an application letter, remember that you probably have competition. Your audience is a professional who screens and hires job applicants—someone who may look through dozens or even hundreds of other applications on the day she receives yours. The immediate objective of your application letter and accompanying resume is to attract this person’s attention. Your ultimate goal is to obtain an interview. As you write your application letter, be sure you complete three tasks: catch the reader’s attention favorably, convince the reader that you are a qualified candidate for the job, and request an interview.