Fun topic. This is my least favorite part of landlording... here's what I've found.
Going back to the initial post and the 'lots of applicants'. I tell applicants that I need an application before showing, or they can bring out a filled application to the showing. This saves me a ton of time. I also try to put a youtube video of a walk through online, and this answers a lot of the simple questions.
As far as screening goes. No one is perfect, so you can always find a clean way to turn down a tenant such as 'not wanting to sign a long enough lease... Unable to get in touch with previous landlords... Does not make enough money... things like that, but only if they ask for a reason. I've learned that saying no quickly if you have any doubts helps both parties... even if you have more vacancies.
Gut feeling: I think this is very important. The one time I let a tenant in without meeting them in person... just phone calls and reference checks, it was the worst tenant experience yet.
I like Brie's idea of meeting them to form the first impression, but I don't think I'll be able to use it since it saves me so much time reviewing applications before going to show the place.
So, what does an apartment in Boston rent for?