In general, how do federal examiners react when they discover we aren't following our internal procedures, but are not necessarily violating the law?

Depending on what it involves will be the basis for thier reaction.

That situation is generally uncovered by internal or external auditors, and like Randy mentioned the regulator's reaction will be based on what is/is not being done.

The examiners will review the audit reports ane management responses. Sometimes, if there are mitigating circumstances or compensating controls, there will not be an issue other than why doesn't the bank re-write the procedures.

I'm thinking of things like bank procedure requiring a written application for all consumer purpose loans or requiring customer signatures on RESPA and TIL disclosures that are not required by regulation. What if it tends to be certain branches or lenders that consistently do not follow bank procedure?