How to establish a global authority to deal with academic plagiarism?
I'll try to shed light on how a Russian group of this kind, Dissernet, works. They run full texts of the theses through their own homebrew plagiarism detection system and employ volunteers to examine possible cases of plagiarism and check the proper attribution of quotes. As their call for action describes, checking a single thesis requires:


obtaining a digital full-text version or OCR'ing a paper copy
running a plagiarism match
searching the Internet for possible sources of misappropriation
preparing a report on the results, filing it in the database and giving context to the results


Apart from that, running a society of volunteers requires:


running a server for reports and databases
paying for full-text theses access 
paying for OCRs and paper copies
paying for commercial plagiarism detection software to complement your own software
paying for legal professionals, mailing expenses, logistics and running the office


In three years from 2013 to 2016, they have produced around 1300 reports, making a living on community donations. At any given moment of time, they had 10 to 20 volunteers active. This might give you an idea for the scope of effort in these kinds of projects.