Probably too small of a sample set here on BP, ask your lawyer or CPA to review

As a landlord, sometimes I have prospective tenants apply before they’ve set foot on the premises.

Staying in front of things will give you & your tenants more peace of mind & minimize problems on back end.  

We do our best to help set them up for success with many tools and resources made available to them.

This credit amounts to $1,666 per month, with the monthly rent set at $3,300.From an accounting perspective, should the $1,666 per month be treated as a liability (deferred credit) and excluded from income, or should it be recognized as income and then applied as a credit at closing?

If you hired an agent or a broker to work with you, you'd be covered - but regulations & laws vary from place to place.Screening is best done by establishing a set of guidelines to qualify applicant tenants, then sticking to those rules to avoid legal issues (and for your own sanity).

What should I expect and how should vet/set up a lease through a temporary housing company for a tenant?

You need to set a deadline for them to correct the issue, then follow up with an inspection or other method to confirm compliance.

You are possibly setting yourself up for immediate failure.....there are too many moving parts and too much money involved to mess up this facet of the project.

Commercial lenders are not playing by the same set of rules as conventional lenders.