The reality is that you can't make people to care more about quality than their (yours) management cares about it. I would suggest discuss this with manager, a

The reality is that you can't make people to care more about quality than their (yours) management cares about it. I would suggest discuss this with manager, and if he cares enough about quality, he can try to slowly coach the individuals to give better reviews. Or he can suggest that multiple experienced/reliable people also review the work.