Being a great player doesn't always equate with being a great teacher. World champions have coaches; if the coach was that good, why isn't he the world champion? Often a good player is naturally gifted, and finds things so easy that he can't understand why his pupils struggle. Empathy is something a teacher needs.
Being on the same wavelength as his pupil is good. Being able to communicate in a way that is easy for his pupil to understand.
Inspiration. If I could bottle it, I'd be a millionnaire.But, can that teacher inspire you? It's a very subjective, inter-personal thing. Even a great teacher may not inspire all his pupils all the time.
Knowledge. When you ask a teacher a searching question relating to something you're studying, an immediate, accurate answer is probably expected. If not forthcoming, is one waiting for you, next lesson?
Qualifications. Not convinced that just because someone has taken the time to study, and may be good at passing exams, that they're necessarily going to be a better teacher than someone who's gleaned experience by being in the industry for years, but has no exams passed.
Age. A young teacher can be more enthusiatic, trying harder to build up his bank of pupils. An older one may be way more experienced, and have more time to give, and will have met far more different sorts of pupil, and therefore should be more adaptable.
Facilities. Do you need to get some recordings done during lessons? Do you want to be able to try out different kinds of instruments/equipment with some guidance from that teacher? Do you want him to organise ensembles for you to join in?
There are so many different facets to this question, and its answers, dependant on the pupil as much as the prospective tutor. As @amalgamate rightly points out, 3 or 4 lessons should be the bare minimum before deciding - unless you're convinced you made a mistake after the first!