Oh là, where to start?! I guess I can only share what is, to me, a good yoga teacher given there will be as many opinions as there are people.
// Kind and open //
Ideally, a teacher provides a nice and friendly environment to walk into. Some students are regulars and there is a certain camaraderie amongst them, which is great, but to avoid a certain air of "clique-ness", the newer students should be made especially welcome. It simply takes for a teacher to introduce her-/himself and have a quick word with the newer students ("Have you done yoga before?"; "Do you need some blocks?"). For me, an approachable and friendly teacher goes a long way.
// Knowledgeable and skilled //
Of course, this is not only about caring about people who come to class or having social skills, although these are absolute essentials!
Knowledge is key and here again, everyone's needs will be different. I like a teacher who can offer a good mixture of yoga philosophy and creative physical practice. So to a good extent, the Jivamukti-style of yoga is one I come back to often. I have attended classes with different teachers of this style whose level of experience varied and yes, I do have my favourites, but I have to say, they were all good and were obviously passionate about what they do.
A good teacher, to me, should also throw in some physical challenges - why not, while my body can still sort of handle them?! - and that is how I fell into the Dharma Mittra tradition. You know all these pretty insane and mind-boggling poses you see in some books or on YouTube? Well, that is what you would work towards! Because of the difficulty of these poses, as a student, you need an experienced guide and specific instructions so that these challenges don't turn into injuries. In this style of yoga, it is important to have a teacher who knows when to encourage you to deepen a pose safely if you are slacking off and when to incite you to back off if your ego goes all out to force your body into a pose.
// A sense of humour //
While I am not expecting a comedy show when attending a class, I absolutely love when a teacher brings some lightness into this all together rather serious practice that yoga is. It lifts the atmosphere, makes people bond over something quirky or funny and it might even help you get more easily into a pose by sort of trying less hard, using a better ratio between muscular effort and bone structure.
// Inspirational //
A good teacher inspires you to encompass the principles of yoga within your sadhana (practice) and more importantly, outside the yoga studio. The inspiration given can be verbal - some teachers are incredible speakers, managing to express complicated concepts in accessible terms and in thus doing ultimately touching your soul -; the inspiration can come from a creative flow of sequences - wonderful for me as a teacher after 12 years of yoga practice - or it can be in the form of wonderful spot-on adjustments. A pose you would not quite get into by yourself despite your best intention finally opens up to you and understanding of this pose settles in, "Oh wow!".
Ultimately, a teacher is a guide and you want to make sure that he/she is the kind you are looking for. The bottom line is pretty simple: trust you gut feeling! While it can be difficult to find all your needs fulfilled by a single teacher, nothing prevents you from having several ones. Happy yoga-ing ever after, everyone!