Mutual interests are a given. Aside from that, is there something that you look for in an applicant to either accept or decline?

When I was an active dom, I made my interests, limits and prices known upfront. When an email or phone call came in, I'd ask open ended questions to see if there was a good connection and learn about their interests. One thing that I'd watch for is someone who contacted me too much before a session. It was almost always a sign they wouldn't show. For the most part, this worked well. After a few years of tweaking the qualifying process, I had a near zero no show rate and close to 100% of return of super fun clients.

Although it might not seem so at first glance, thorough vetting can work as much for the sub's benefit as the Domme's. Insuring a good fit and a sufficient number of mutual interests go a long way to avoiding a disappointing session.
I've always been reassured by a Domme who asks lots of questions before a first session.

I've only had 2 professional sessions. It was easy to get booked. I filled out a request form and my girlfriend talked to the ladies on the phone. Maybe it was an easy process because it was a woman talking to another woman. I never thought about the security aspect. My guess is that is a major concern.

You were a lucky lady!

Security is probably one benefit of working for a house of domination or renting space from one. Honestly, I'm not too worried about it. Someone would have to be an absolute idiot to book an appointment through an easily traceable method and then hurt someone.

Everyone is bound to be different. Pun intended. ;-) But, I tend to agree with Lady Cheyenne on this one. I wouldn't want to see someone just for the money. There would have be a good connect.

Mutual interests, ability to follow directions, politeness. I do not accept sessions with people who rub me the wrong way, even if they technically follow all the rules. Dominating people I can't stand is a hard limit.

Obviously this has to be about a first session. Usually I try to make clear in my email things I expect could be a problem for the particular mistress. Nobody wants to get into a situation of incompatibility. I always like to talk a lot before starting. I do not mind adding that to the time of the session. A first session is an investment. Usually the payout comes in the future.