Ideally, a second review (and sign off) should be occurring in the business unit prior to your review (assuming your have a compliance role).
When we do our testing/monitoring, we review the denial reason and ensure that the business unit performed the second review. I don't feel that it is the role of compliance to second guess denial reasons when there is someone else in credit performing a second review, but you can look for obvious things.
Delinquent credit - review the credit report
Insufficient collateral - review appraised value
DTI - review calculation and compare to underwriting guidelines
Aside from that, we read the credit memorandum to ensure there are no statements or information that would suggest a fair lending problem. Comments about a prohibited class or comments about the area a property is located (redlining). And of course, review any written AANs for proper completion.
In the current environment, we're definitely looking at details of appraisals, including all text, not just valuations, when an application was denied for collateral.