First off, they shouldn't say no credit checks if they're going to check credit; that's just wrong.The majority of lenders will run your credit because it is the best indicator of what kind of borrower you will be. 

FWIW, it is fairly normal in Denver to have it listed as a 4 bedroom, and to indicate the non-conforming status in the comments.  

Also, this wIll give you an indication of how the property will perform should you decide to move out when you fufill the FHA requirements.

If market research indicates a particular area is losing jobs faster than the national average, has a low population rate to begin with, and has a higher proportion of owners to renters, along with other indicators of potential issues, then I may be able to reasonably assume that it will be more difficult to find good tenants, more difficult to charge market rents, etc.

I totally ignored them at first, but more and more they are showing themselves to be a surprisingly (to me anyways) good indicator of how much room for improvement a property has.

The only thing that comes to mind immediately is "water marks" on the wood hidden behind a wall in the basement which indicate it was previously wet and dried.

They indicated that there were no oil tanks on the property. 

I know you mentioned that the tenants pay water and sewer, does this also indicate that these services are provided by local/city utilities?

Try to have the contractors provide you an updated invoice indicating paid in full/ work completed.  

@Joseph LuceI agree with @Tim Gordon for the reasons he indicated.