For a school or any business to truly work well, everyone has to feel respected and appreciated. From the head honcho to the cleaners, they all have to feel they have a part to play and are contributing. Often foreign teachers don't feel this and feel they're only at the school because that's what the parents want. Make all staff, including the foreign teachers, feel welcome, valued and respected, and they will work harder and more happily. But this really is common sense.
The buck stops with the people in charge. These people are paid more and are usually employed based on their qualifications, skills and experience. The biggest skill a boss can have for me is compassion and empathy. Bosses can't simply demand and order. People don't respond well to this. Also, the boss has to be consistent. Either you're an asshole or you're not. There's nothing worse than having a boss who blows hot and cold. People don't like unpredictability. They like to know what to expect. At least with an asshole boss you know what to expect and what's expected of you.
I feel agencies will become obsolete. We live in an age where we have instant information at our finger tips - BUT, schools need to put trust in their teachers. Identify the good ones and utilize them. Don't chuck them all in the same pile because that will breed complacency. If you have a decent teacher, in everyday on time, accommodating and affable, put some trust in them. Give these teachers more responsibility. Have them help with recruitment. Make them feel valued. Once they prove to you they can do it, have them as a head teacher.
Once they have been appointed as head teacher, they can recruit new teachers. They can monitor and check on new teachers. Pay them more and maybe decrease their teaching load so they can concentrate on leading. But! Very important - make sure they're still teaching. The best way to lead is from experience and setting examples. "I might be your boss, but I do the same teaching as you. I know all the problems you have, and I'm here to support you".
Deadbeats and jobsworths need to be identified and culled. There are too many in schools nowadays. I believe most people are good. You treat them well and they will reciprocate that. The TEFL industry here needs a huge kick up the arse. We need to get away from thinking of education as a business. Education is not something that should be allowed to be bought or sold.