Sometimes when you look at the deal your numbers does not match. 

I recently received a loan proposal from an American financial LLC - somehow there are things that do not match on my humble opinion.

Should I shoot to have my offer match or below the assessed price?  

It's that buyer, and/or one looking for many bedrooms that is probably a good match for the house.

@Annette Ammarell, it would make a great match.  

So their prices are realistic, but you still have to match comparable properties the best you can (also not perfect if no similar ones are being offered). 

If put 10% skin in the game and give them an interest rate that will match their current passive rental income, with the agreement that I can refi in 1 year do you think anyone would be interested in this arrangement?

This makes for a great community based support system for government activities.Check into economic development funds at the state level, identify the enterprise zone and request funds that are available, then more funds on a matching basis from your bonds.

Take pictures, then match with invoices (i.e-if they charged you for a new hot water tank but the ones in the property clearly are dated)If there are Sec 8 or DSS tenants that possibly were placed there, you could check with the agencies and give them the addresses of the properties and see if they had been paying rent payments for those properties (note: they will NOT give you tenant info, but at this point you probably just want to know if there were tenants in there at all).  

Buy the drywall AFTER you see how thick the existing material is so you can match the thickness of the new drywall to the old stuff.