If they had one 30 day late over the history of their credit, not a big deal and is a 1 point deduction, but if they have 4 they lose all the points in the category. 

I think the landlords will take a look at your background, credit, income, etc. and will conduct a good interview with you to see if you are a good fit.I would provide the landlord with a solid past history, references, employment records, etc.Most rowdy single guys are the ones who don't have a high income and a solid background, in my experience

Here are out miniumum requirements:Minimum Requirements: Applicants must make three times (3x) rent in incomeMust show proof of income (Last 30 days of pay statements or other income)Applicants must have suitable criminal history background results determined by property managementApplicants must have suitable credit history.

Does it show positive history since the eviction?

My attorney feels this is a MAJOr red flag2) the seller does not have proper pay history on current tenants stating that the property is so small they did not keep this kind of documentation. 3) I saw the property and it visually looked good.

The background check is comprehensive and includes credit, evictions, judgments, address history, sex offender, criminal background, etc.References will be checked.Rent is $910 per month, $910 security deposit.

Interestingly, 2nd and 3rd floor units tend to sell for higher prices but perhaps aren't as desirable in the rental market.Looking over rental histories, jan-mar rentals seem assured but we're not sure about the high-value, summer rentals.thoughts?  

However if someone were you pull up the records they will see the history and note that the prior owner was you (before the land trust).

The website keeps a record of all payments for you and the tenant to see the history. 

If you have different criteria (credit score, eviction history, etc.) and they don't meet those, you can absolutely deny them.Personally, I haven't seen many applicants apply with a rent voucher and also have a solid credit score so this shouldn't have a lot of impact.