one thing that can be and probably should be changed is a "NOC letter" issue. NOC should be given to the employee authomatically in two cases: when his contract either completed or terminated. That is all changes that we need so far. Other than that there are no any real problems with sponsorship. Don't forget, sponsoring companies bring you to Qatar, and they are totally responsible for you. So they kind of have to have rights to develop some tools to be aware of your movements (up to some point).
As for exit permits, as i am aware, all (or most) western companies issue Multiple exit permits for their employees.