Well, i can't give an answer because you're being so vague i have no idea how to answer. To really know for sure would depend on what these 'bad mistakes' are.
But i can comment on the distinction of forgiveness vs consequences. See you're operating under the idea that forgiveness also means forgetting. I can forgive someone, as in not hold a grudge, bitter feelings, anger, resentment, etc.. But at the same time have an awareness that they are not someone good to be around, and and not want them around me to continue their negative behavior.
I'm not sure what the issue is here, but i would say a schools first and foremost priority is protection of the children in their care. And if there are teachers who are making a bad environment, or bad example for the children, then removing the source of the problem is the schools responsibility. People are trusting you with their children and that trust should be kept as utmost importance. And doing that does not mean it has to be spiteful or unforgiving or vengeful. When your children disobey, do you 'just forgive'? Or do you teach them? Perhaps provide consequence?
Also, it is biblical to forgive, but the bible (and most christians love to forget about this) also expects us to maintain standards in our lives, our church, and anywhere else. And when someone comes against those standards it is biblical to 'cast them out' so to speak. And by casting them out, its not vengeance, or unforgiveness, its out of hope that they learn, and come back repentant.
But as far as any specific recommendations over this particular situation. Well, whats 'bad' to you may not be bad to another. Bad could be varied as well. Bad could be something smaller like a teacher losing their temper and yelling, maybe using a few cuss words. Or bad could be finding two teachers having sex in a classroom after hours. Both are 'bad' but both don't deserve the same treatment.
Lastly, you many want to move this to another section. This is the area for new people to make introductions of themselves as new users on the site.