I guess you are asking about red flags other than the obvious unprofessional issues. For me personally, a red flag would be a therapist who discloses their own personal stuff way too early (and no particular reason other than -- I'm guessing -- to somehow let me know they "understand"). I find that creepy and TMI. (Disclosure down the road in very small and very focused doses is fine. It's the baring their personal history early on thing I'm talking about.)

The other red flag for me is simply that I just don't feel a darned thing in their presence; it is as if I might as well be talking to a fence post. I need my therapists to have a personality -- the whole blank slate, unemotional, detached thing doesn't work for me personally.