The different ministries will determine the legal framework in which you can provide your services. But they do spot checks.
There are health and safety measures you need to keep in order. For instance, fire extinguishers, escape routes, and those things. The Fire department comes once a year to make sure all is in place.
MoE has a whole list of documents and paperwork you need to keep in order on a daily basis. There are documents that you need to hang out for everyone to see. Business Licence, Teaching Licence, Terms of Conditions and a list of all the teachers that are employed. If you do not, you can be fined up to 500.000 won per document not visible. You also get a strike. Three strikes and you have to close your business for a month. When you have a bus to transport students around, you need to keep your paperwork ready, and your insurance on speed dial. MoE will also require you to visit their “meetings” to inform you of safety standards, twice a year, and now they added a meeting to teach us how to drive the van.
Immigration doesn’t do spot checks, but they do get iffy when you don’t do the proper procedures for hiring and firing people. The hiring procedure is pretty straightforward, you collect the documents, put down the request, if accepted receive the possibility for your teacher to enter on a E2 visa. When the contract ends, you still need to deal with Immigration, by ending your sponsorship of the E2 visa.
The government only “reacts” to problems. They seldom go out of their way to disrupt your business. The key is to make sure that you don’t become a target of their control. I was checked three times in my 5 years of operating. The first one was when I just opened, the second one to make sure the adaptations were correctly made, the third one after one of my students filed a complaint on a rule I didn’t know existed. That one cost me 1.3M won.
There are quite a few obscure rules that are not mentioned when you start your business. MoE, Immigration and all other departments make the assumption you know everything. They will not inform you of all the details, too much work for them, and not really their problem. The responsibility lies with you to get informed and keep questioning, even if you think you got all the answer, there is always something a little bit more.