It's advisable to thoroughly document your application and screening procedures, ensuring consistency for every applicant.

Would diligently screening them limit the risks of tenants damaging the property?

These included one of the outdoor lights not working, small common area repairs, tightening things, and a hole in a screen.

Go to BUILD YOUR TEAM at the top of your screen, and you can search for other MEMBERS or LOCAL MEETUPS.

This new one on the left really makes the forum discussion area small...The forum area used to take up about 90% of the screen, now it's about 50%.

Second, you can take this opportunity to have a conversation with the current occupants and make sure you get all of the people living at the property screened and added onto the lease. 

Thorough screening and understanding of your tenants.  

Perform the same task in each app to ensure a fair comparison.Load a property with pictures and details.Market that property.See what your marketing looks like from the public's perspective.Submit a fake application to see how easy the process is.Run a credit/screening report on yourself.Enter a maintenance request, assign a vendor, and attach a fake invoice.Enter charges to the tenant's ledger.Enter recurring charges and automatic late fees.Sign documents electronically.Run owner reports.After testing a few apps, one should clearly stand out.

I needed a small 10x15 lanai re-screened.  

Quote from @Andy Ramos: It is not illegal, but it is unreasonable.The leasing fee covers all the work associated with moving the old tenant out, supervising the turnover, marketing, screening applicants, getting them under contract, moving them in, etc.