After my last therapist moved away and I started to look for a new one, my initial search was to weed out those who practice short term therapy, anyone who mentioned CBT or any of the other "evidence driven" therapies. I ended up calling the therapist of a colleague that they had raved about, and that therapist gave me 3 referrals because she was not accepting new clients. Of the three referrals, one was big into testing and helping people pursue career goals, another was too gooey in her profile (lots of talk about the healing journey and stuff like that), and another (the one I see now) was just right, from the initial phone call to first session. I made sure she did long term therapy and did not use pathologizing terms.

I don't think I ever saw a therapist who had overt red flags. If there were concerning things, those did not come out right away, unfortunately.