What should I do if I think a researcher in my university is intentionally employing incompetent people?
My suggestion is that you let it go for three reasons:


This is hardly the last time you'll come across this problem, inside or outside of academia.
There are factors here you might not be considering or know nothing about.  Maybe the person you're tutoring in math has excellent people skills, or is the instructor's nephew, or the Dean's. Whatever the reasons they're really not any of your business.
As you say, you will indeed end up being considered a malicious and jealous man.  


If it really bothers you you should probably find somewhere else to work where this isn't a problem, but then see point #1, above.