Proper screening avoids a lot of problems. I tell plenty of people that their application is denied. It saves me a lot of problems later and protects my properties and the owners from expensive repairs. It sounds harsh but I can't care about everyone's problems. If they have to explain their situation to me I most likely will not rent to them. I'm not willing to make other peoples problems my problem by taking them on as a tenant.
A good way of finding out if a tenant will be a problem is by letting them talk. A lot of renters don't realize landlords are essentially looking at a renter as a business partner. They think landlords are in the business of providing housing. That is not the case. Landlords are in the business of making money from cash flow and appreciation. This can be most effectively done with a good business partner or in other words a good tenant. Potential tenants will call me all the time and before they even see the place or fill out an application they start telling me all their problems and explain to me why nobody wants to rent to them. After letting them talk I usually know I no longer need to waist time with them and I kindly explain that it doesn't sound like they will fit my guidelines and I wish them good luck.
I'm also amazed how many times I get a partially filled out application. When I tell the person they need to finish filling it out and resubmit it some people get mad, others never reapply and some even resubmit another incomplete application. My application isn't that long either. It is one legal page long and only asks for essential information yet they must think I don't really want the information, or that I don't need it or they don't want to tell me. Either way it must be filled out right or the answer is no. Weirdly, tenants and prospective tenants have to be trained to follow the rules. Anyone that can't respect the rules is not someone that I want as a tenant anyway.
One BIG red flag is if they are not able to pay the security deposit in full. If they need to pay it over time the answer is ALWAYS no. If their finances are that tight then they will have a hard time paying rent on a month that the car breaks down or something else happens. When I tell people,"no I will not let you pay the deposit over time" many times they respond, "that's ok I can figure it out myself." I always get a laugh from that response. I think if you can then why were you asking? If you don't make their problems your problem they can usually figure it out themselves and if they can't you don't want to work with them.
I find it is important to never give in to an applicant. It lets them know you won't be a push-over landlord and some people are looking for a landlord that is a push-over.
Some may say I'm too "tough" on applicants and tenants. I say I'm only expecting people to act like an adult in the grown up world. I expect people to fill out a complete and accurate application and then I expect them to live up to the lease, just as they would expect me to live up to what I agree to on the lease. At the same time an applicant is a potential customer and needs to be treated with respect and they need to feel like (until I know differently) that their business is important to me. Being "tough" doesn't make it hard to fill a vacancy either. I can usually get a place filled in a few weeks or less.