The first thing I look for is patients. I hate T that tell you that you have to be better in a certain amount of sessions and that's it. 12 sessions and your out the door, like everyone's problems can be solved in 12 hours!!
After that its a mixture of things. One thing that's personally important to me is their religious background, but that's just me. Professionalism but still being laid back enough to put me at ease and help me talk. Knowledge and experience in dealing with people like me (because i'm definitely not easy to deal with

) How easy they are to contact and help me if I am in a crisis and a bunch of other things.
There are a reasonable amount of T in my area but I wanted one with the same religious background as me so that limited me to 4. The first one I saw my church paid for so I was stuck with him. I got married and my husband has amazing insurance so I got to choose my current one.
The first T I saw was horrible. He was extremely pushy and wanted me out of his door in X amount of sessions. I think I ended up worse then when I started with him. It took me about a year to even consider therapy again after that.
My current T is amazing. He works well with me. We just clicked at the first session. I am one of those people that doesn't really like to talk in therapy but needs the therapy so the T ends up having to fish around and ask a bunch of questions before I end up talking and he is so patient with me. Sometimes it takes two or three sessions to get down to what is really bothering me but my T sticks it out with me and we get there.
I think if your having doubts about your current T then its probably time to start looking for a new one. I dont think there is a "right" way to do therapy. I think everyone is different and has different issues that they resolvethem in their own ways and in their own time frame. Find a T that understands that, someone that understands you and what you want to get from T.I hope you find someone that works.