Ensuring thoroughness means that you do everything you can to avoid not leaving things out, not making mistakes, working to double check everything, and verifying facts, etc..
I used a bank analogy for auditing and ensuring thoroughness certainly applies.
However, there are other types of "audits" where ensuring thoroughness is important.
Consider an airplane and a pilot.
Pilots use their own sort of audit: a pre-flight checklist before taking off. (Actually one of many checklists.)
Very thorough because everything is checked from fuel tanks to switch settings.
Very lengthy written list that goes step by step to ensure that the airplane is correctly configured and ready to fly.
And often done with the help of a co-pilot to observe the process and again double check everything.
= = = =
An even better example of "ensuring thoroughness" - watch a rocket launch as they go through the pre-launch countdown.