My organization a while ago saw significant issues with untested fixes being deployed and similar bad practices (undocumented configurations, lack of integration testing, etc.). The thing that did it for us was seeing our up-time drop below 99% in production systems. It became downright embarrassing and started costing us real $.
So our then-CIO froze all production changes for 90 days. In that time, we instituted a change review board. They now approve all production changes. Without the culture change that came with the culture freeze, the new process might have failed. But we bought into it. And by putting them in as the gate-keeper, we now require documented QA approvals.
So in your case, a Change Management process like this would help. But you'll also need to change the way people care about your production environment. You'll need both, but take heart - it can be done.