1. Is the instructor still learning?
In my opinion, this question is even more important than the question “How much does the instructor know?” If the instructor is very knowledgeable, that’s great, but it can be nearly impossible to precisely quantify how much knowledge the instructor actually possesses.
If the instructor is constantly striving to expand his/her knowledge, by continued training and studying (in other words, they are still a student), then it hardly even matters how much they know right now, because they are learning and growing all the time. Each day they will have something new and exciting to share with the students.
Such an instructor is likely to be passionate about all aspects of the martial arts, and give his or her best when working with you. Since the instructor is still a student, he or she will have a helpful perspective and insight into your experience as a student, and can help you manage common pitfalls and challenges along the way.
Finally, I believe that instructors should always strive to continue learning because the martial arts are constantly evolving. New material, and new ways of teaching old material, are constantly being developed.
2. The other students in the class
The other students in the class might be even more important than the instructor, with regard to your progress. You and the other students will be interdependent upon each other for your growth and learning. If the other students are focused, hard working, and dedicated to their training, it is very likely that you will be able to make tremendous progress. The instructor can provide direction and knowledge, but only students, working together, can execute that knowledge and put it to use.