Am I missing a big obstacle or law that makes this not a good option?

As for your DTI, you won't be able to count income from roommates in your own house, so that might be an obstacle if you can't qualify for both payments on your own.  

I would love to network with any investors involved in those areas.My initial obstacles in my area have been the inability to acquire thorough rent rolls and the applicable cap rate for the particular market.

We are supposed to close on June 27 but now our lender says he can't close until the detached garage is painted and roof replaced.

The roofing company said it has "extreme" wind damage and basically said insurance wouldn't be an obstacle. 

If I were starting out I would look for a detached duplex that has a value add that can be finances via FHA loan.  

This allows for an auxiliary structure (so potential to turn the detached garage into a carriage house... permitting dependent). 

I know some MLS have detached from Zillow (with good reason - Zillow is horrible and unreliable ... anybody can post whatever they want there). 

What kinds of difficulties will we face if we purchase and rent the property despite this obstacle?

If markets are flat or deflationary, obviously it make less sense.Even if your local market is appreciating, in many places across the country, housing prices have become detached and continue to diverge from rents (and are increasing faster).