The apartment was not cleaned, she left a bunch of her stuff as well (furniture, mattress). 

@Ray Harrell My  net rental income comes in at 4x my regular W2 job, so I'm not too worried.

In the corners they tack some small 1/4x 1" boards to clean offI purchased an 8 unit property consisting of 4 duplexes.

You might go to a Lawyer/Attorney that regularly working on Partnership and he could probably tell what is the best way to go.I think that various books on Partnerships would help you make the right decision. 

If it goes down, they can not purchase and it would not be any different than if we had a regular tenant.Am I missing something here? 

Had the pleasure of cleaning out junk from the property of my first deal and working on the landscape.

What is the best practice to keep a clean and efficient system for screening peopl

One thing you seriously have to consider is whether the turnover/vacancy involved would have a big impact on your bottom line - for example does your property manager take 1/2 a month rent to find a new renter, how much would you spend in cleaning/paint/carpet/etc between tenants and if it is a cheaper property in the area, are your tenants going to maintain the property well? 

But oil furnaces require more cleaning and maintenance . 

Here are some alternatives to commingling your assets:using the Solo participant loan feature to do the deal outside of retirement fundsusing non-recourse financing from a lender or private source in combination with retirement funds as the down paymentusing your 401k or IRA and partnering with non-disqualified persons I'd recommend you reach out to a few providers who regularly post here on BP to get a better understanding of your options.