The 3rd unit tenant is a smoker, smokes inside the unit and pays $720 and the 2nd unit tenant is paying $995. 

Pooling resources, this is a very sticky area, I'd say most know that an "investment club" you know 12 little old ladies or phat cigar smokers have to register with the SEC to buy securities, putting "investors" together to buy mortgages has the same requirements and if you're in a management position, welcome to the brokerage business. 

I do NOT allow smokers.

Many heavy Drinkers (and smokers) in the Military, back in the 80's.After 2 1/2 years,  I not only had enough to put a large down payment on a nicer car (Shiny Object Syndrom), I also had enough saved to go on a 3 week trip all over Europe. 

From a screening risk profile, this kind of relationship drama happens more frequently with unmarrieds vs married, smokers vs non, etc. 

we recently purchased a house where the previous owners were heavy smokers and the house wreaked of smoke.

If you have an outdoor smoker, will the inside of a property smell?

That's where I set deposits for smokers now.

I've had two occasions where the reference they listed told me not to rent to them because they were violent, late payers, or too needy.Not doing a criminal, credit, background check, which might have revealed criminal or credit problemsBeing slow to evict (mentioned by others)Believing their sob storiesAccepting partial paymentsFailing to document every conversation or interactionNot walking through the property to make sure they're taking care of it (I now walk through every 9 months so I can see problems in different seasons)We've found crack pipes and other paraphernalia after they moved outWe've discovered piles and piles of trash (some bagged, some not) in closets, basements, sheds when trash cans and pickup service are included in their rent - all they had to do was carry it out, at no cost to themWe've Found smokers, pets, extra peopleOverall, I've had great success as a property investor. 

If someone’s qualifications on the app don’t meet your requirements (income not high enough, smoker, pets in a no pet rental, desired move in date doesn’t line up with when you want the unit filled etc) why would you waste time on a background check?