I agree with Elizabeth about the detailed lease. It allows you to create expectations and when they make illogical requests, it's extremely helpful to be able to point to the words in writing that they've already signed off on. Regarding the requests for showings, I put the requirements that I am going to need in the ad for the property. In MN, you are required to notify prospective tenants of what will qualify them prior to application. For example, in the property ad, I write: qualified tenant defined:
Credit score of 580+
Monthly income 2x rent amount
Positive previous landlord reference with no money owed
No felony convictions or violent crimes
This is not to say that there aren't exceptions, but any applicant not meeting this criteria as it's spelled out can be rejected. This really helps to weed out those who wouldn't qualify and greatly reduced my number of pointless showings. I also reiterate it when setting up the showing via email.
Hope this helps!