I care that they make more than bare minimum effort.
I care that they take my own knowledge into consideration. Two heads are better than one.
I care that they are able to be honest with me, and are able to work with some degree of transparency.
I care that they understand the need to avoid conflicts of interest, and do so.
I do all these things for them, and am not even getting paid. There might be other things I'd "like", but as I've yet not even been able to find more than two out of these four qualities in a single therapist, I can't even get that far.