The answers posted do not match my experience in the past. They may be correct in some scenarios but lenders I have worked with have not been as liberal. The following reference seems to most match what I had found -even though it is written for the UK
What makes a property unmortgageable?
It is always sensible to check on the mortgageability of a property before bidding on it. But as a rule of thumb, the following situations will likely make a property unmortgageable.
• Properties without a kitchen or bathroom.
• Properties with any kind of structural defect, damp, dry or wet rot.
• Properties close to mining works, areas of landfill, areas of recent flooding or subsidence.
• Leasehold properties with a short lease, typically less than 70 years, or a defective lease.
• Where there are boundary disputes or where planning applications have not been applied for correctly.
• Derelict property or where part of the building is in severe disrepair and needs demolishing.
• Properties of non-standard construction. Standard construction has brick or stone walls with a roof made of slate or tile, so anything that differs from this will be classed as Non-Standard.
• Some properties with sitting tenants or regulated tenancies.
• All properties with a value below a threshold, sometimes stated as £40,000.
In particular the item:
Properties with any kind of structural defect, damp, dry or wet rot.
That is more restrictive than the other answer and comment - and also more along the lines of my experience (with a couple dozen lenders in several states). I'm not sure if that means there do actually exist lenders as lenient as the other answer suggests. I will be looking more into that.