I recently accepted a prospective tenants application for one of my rentals.

Hi Marc -It is generally acceptable to summarize your activities in your log.

We put in an offer yesterday that was accepted so hopefully this is a good step in the right direction. 

You as a host are going to apologize for a guest's bad behavior and accept their one star review, because you're afraid that other guests might think that you're "unprofessional" for calling them out on it? 

There’s 7 tests for materially participation.

For example, I mention that every adult must pay a $30 application fee, pass my credit/criminal background, make a combined income of 3x the rent, and whether or not the property accepts pets.

In your next lease ensure that you have a one month penalty for breaking the lease and enforce it along with getting everything in writing when they give notice and you accept it. 

If you pay more, you won't meet your metrics and will probably have negative cashflow and/or equity.You may have to make 10, 20 or even 100 offers to get one accepted at the price that meets your numbers.

Once you have a shortlist, sign up for an account with each one and test them extensively to see how they function.

I do not have a problem with my pets in my units and have found accepting them to be a big selling point.