@Jay A., while I have not invested in a turnkey property, I have viewed several on some of the websites. Things I would ask:
Full list of renovations that were done, with before and after pictures of basically everything.
I would still get a property inspection, like any house you buy. If they provide you one, I would still say I am getting my own.
I would ask for full demographics of the area, including incomes, home prices, education levels, crime levels, etc.
I would want to see full tenant application and any pertinent backup verifying income, employment history, landlord references, etc of the in-place tenant.
I would want to talk to the property manager, if they are coming with the property. Understand their fees, bid process, termination requirements, markups for work done, how they confirm fair bidding (especially if they have on-staff handyman).
I would talk to the actual tenant in place to understand what their experience is with both property and management team.
I would drive the area to understand how your property compares to others on the street/in the neighborhood.
I would talk to other management companies and realtors to understand their understanding of the market, rent levels, etc.
Basically, full due diligence and underwriting of the property. You are effectively paying a premium for someone else's work, and taking on all their risk, so I would make sure to understand as much of the risk as possible.
