I believe the person has to be Shomer Shabbos Yid. If the Mashgiach is Chas VeSholom seen violating Shabbos, he would likely not be allowed to be a Mashgiach.
You have to define what you mean by morally corrupt. There may be an issue of Neemanus.He may not be a viable person because the Mashgiach has to enforce Kashrus, for example in a meat place, usually there is a plate and pan for fish only, not for sale but for the staff, if the Mashgiach sees them cooking the fish in the meat oil he has to enforce that the oil gets changed.
There is also alot of ‘look the other way ‘ opportunities because
in a very bad economy there is much competition for these jobs witch can present a possible conflict of interest.
So someone like you describe may not be best but it depends I have seen many people in food industry personally OTD but take the Kashrus very seriously. So this man as well.
It depends i guess is he publicly known as a criminal or not.