For example, the other day I realized I had a setting on my PostgreSQL config that allowed certain hosts to connect without password auth. I'm wondering if there is/are a collection of standard, beloved and essential security assessment tools (or checklists) to find weak spots in my server so I can plug them before someone else does.
I would recommend looking at the NIST National Checklist Program Repository which contains checklists and security baselines for many systems. You would probably need a SCAP tool to analyze your systems. You can look at Retina community edition, which will let you upload baselines. Check this link http://web.nvd.nist.gov/view/ncp/repository