The other question worth considering would be is there an established divide between public and private sector corruption. I think that you'll find there is a large amount of cross pollination between the two.

As for a couple of general examples of corruption in public education
- tofu dreg construction
- differing admissions procedures and/or 'sponsorship fees'
- academic corrupition i.e. plagiarism

There are direct links to these problems and the working conditions of foreign teachers. It's also worth asking yourself whether you think an institution that is willing to skip on construction costs leaving teachers and students in dangerous buildings (and then pocketing the difference), taking back handers from parents to get their kids into the best schools/classes and allowing rampantant and unchecked cheating to occur in their school is likely to be a good employer, honour all the terms of their contract and do what's best for the welfare of teachers who work in such places.