Degree programs or careers with a focus on plagiarism detection? Are there any formal degrees that offer training in tools for detecting plagiarism? Or on understanding fair-use, proper attribution of sources, and avoiding plagiarism?

Are there career options which focus on exposing plagiarism?
Dr. Stefan Weber (PhD in Communication Sciences from University of Vienna) has essentially made a career out of detecting plagiarism, mainly in doctoral and habilitation theses from important public persons in the german-speaking area. You can find some information about him online. He has written multiple well-selling books on the topic, sells plagiarism checks, and regularly appears in public discussions.

However, note that the life of somebody who frequently and very publicly raises strong allegations against professors, politicians, and other degree-holders with substantial influence is not necessarily a fun one. As you can imagine, a lot of dirt gets unearthed and thrown in his face routinely (sometimes justified, sometimes more as part of counter-campaigning by the persons he attacked).

In summary, I think he fills an important societal niche in our area, but I really wouldn't want his career.