So that pretty much kills the anonymity play.I spoke with the mail carrier and she said there is not really a way to stop it. 

[Certainly, that'd be a big red flag for me].Your position is strong, because you can offer your price, or walk away at any time!

It could be a good deal but that's a big red flag until proven otherwise. 

Can you give me some advice on what would be red flags to look for on the inspection reports?

I would agree that broken down cars in the yard would be a red flag it might cost a bit of money in terms of lost rent in the short term but of the long term not having to deal with a potentially uncooperative tenant will save a lot of money.

One of the biggest is that I requested to see the current leases for the property and the past few years Schedule E (as this was an investment property of hers) in order to verify the performance of the property, and she went off that I had "No legal ground to request those documents", but she would provide the current leases AFTER we close.That sent up more than one red flag in my opinion. 

That throws huge red flags for me.

I do them for all my tenants to ensure what I'm getting myself into, and beware as their background may not be clean, and it's highly likely their credit will be bad, but it's more for me to ask them how it got there or if there are any huge red flags.

I am afraid that if I start out with a business type homeowner's insurance it would raise flags with the lender and that a higher down payment would be required or issues would arise with the loan (I don't know for sure).

@Brad Carrier If, as @Jason DiClemente suggested, you have a hard time getting a loan, I'd suggest talking to a local bank or credit union to see if they would do a portfolio loan.These loans are not sold on the secondary market, so they're serviced by the lender.