Based on your post I am getting so many red flags.

Again if you just believe the house is overpriced 90% of the time it is, that's a big red flag right there.Good Luck and Happy Investment!

Also in my area, a sheriff's deed serves as a flag that some mortgage(s) will no longer encumber the property.

Any red flags with "roommates?" 

This is about lap 345 of our "going in circles" maybe we wave the black flag and end the race that nobody can win. 

A Red Flag: I pulled up the parcel record and noticed some irregularities in the sales history.

But, making two applications is a bad idea, sounds like a good one, but it causes issues.Credit inquiries are not the big issue, here's what can be;Bank A sees you went someplace else, the delay working on your app until you explain what you're doingBank B can do the same thingThey will delay settlements to ensure, by verification you aren't getting another loan of any kind, that changes your ratios.Dealing in good faith means a lot to a lender, if they feel like you're just jacking them around, they might reciprocate.If both lenders reciprocate, you're in the cold, butIf you can energize them back into action, you still delayed things and you have pie on your face.This is also an indication of your management techniques running your business, not cool they may decide they just don't think you're ready for their bank from a business point of view, remember this is commercial, not consumer, if they doubt you management/business skills and ethics, you're gone.Biggest flag begins with an attempt of fraud, trying to get more than one loan, usually such attempts will never happen, too many checks in place, doesn't mean someone may not try, so your intent is questioned.How to avoid all this, tell Bank A that you will go with them, but because time is of the essence and because they can't totally commit ask them, inform them, that you'd like to see if bank B could be used to back up the deal.

A family of 4 i can see but 6 or more is a definite red flag.

But regardless, the biggest flag is you net free cash flow is below $100 per door, which is usually the floor that is used as a standard for determining if it is a good deal.

I don't mind having an old AC unit, but having a 15+ year old AC unit being packaged to me the buyer as a "new" unit is a huge red flag.