The hedge fund I bought it from thought it was 300% underwater so they were desperate to get rid of it.

Tenants lie and desperate, irresponsible tenants lie even harder.Definitely serve the Pay or Quit notice. 

In your pre screening you ask:1) Do you presently have a pet of any kind.2) Do you foresee acquiring a pet of any kind during your tenancy.3) Is there any possibility you may need to pet sit someone else's animal.You then inform them that if any animal is found to be in, or has been in, the unit for any reason they will be evicted or assessed a $1000 fee for every occurrence on a per day  bases.Some are stupid but most applicants believe that landlords are so desperate and so dependant on needing a tenant asap they think landlords will ignore their own rules to accept a good applicant.

@Shawnette Ashburne the answer to your question is to secure financing first, the seller won't even look at an offer if you don't have financing in place unless they are desperate.

Take your time, buy when others are (especially when they are desperately) selling.

@Jay Garrison from what you just described, I would say you desperately need an experienced agent.

@Matthew Paul How desperate are you to rent the place? 

The best sellers to target are the sellers that are looking SO desperately to sell their house that they are looking for YOU!

And of course, this was essentially disrespecting the tenants, kind of bullying them since they were desperate at this low end of the market and had no power.

. :) I'm not desperate to accept the first applicant.