During the phone screen after I find out the standard questions I'll say "I'm very good and do a very thorough reference check as well as credit and criminal checks so is there anything you need to tell me about?"

Just recently, we had a tenant where a criminal record was missed.

Complete with credit, criminal and eviction history along with some work history and an income to rent ratio of the client. 

I refuse to believe a large segment of the rental market will resort to criminal activity in the course of paying rent.  

Fails to tell the homeowner that they are actively marketing the property for market value and that the investor or real estate broker plans to assign their rights in their contract with the homeowner to another investor/buyer.Fails to tell the homeowner that they intend to make a profit by accomplishing an assignment of the contract.Fails to tell the homeowner when the contract is assigned to a different investor/buyer.Investigated Case ExampleBelow is an example of a case that we investigated where the broker involved in the deal was referred criminally and her real estate license was revoked.The victim had the misfortune of being on her front porch when an “investor” and his real estate partner approached her and told her they used to live in the neighborhood and wanted to move back.They figured out her weaknesses and used them against her.After “working” on her for a few days, the investor and real estate agent had a meeting with her that lasted hours.

Most won't get to that point and the ones that do have criminal records and bad credit.

Most landlords do not put a lot of value on these types of criminal records because they're not violent crimes.

Criteria list:Standard stuff - no eviction, criminal history, etc.No petsCredit score about 700+Stable job with 3x gross incomeNo smokerAm I shrinking my market too far or is this absolutely reasonable.

For screening, I would focus more on Credit score, rental history and criminal history. 

I use their screening service to screen potential tenants and their reports are thorough including credit, income identification, criminal record and rental history.