Kudos to your students, enwiabe

I agree with your points but just to clear up any misunderstandings, what I was trying to get at as a whole is that tutoring should be active, i.e. the tutor should be actively engaged in promoting student learning outcomes.
For fear of going off onto another tangent, in relation to the OP's questions, I think what makes a GOOD ENGLISH TUTOR is that they actively seek out your weaknesses but also actively promote ways of correcting your errors and avoiding them to ensure that your performance is your best. I'm sure enwiabe will agree with me here.
So it's really how you are as a student. Some ideas are listed below:
What do I want the tutoring for? What role should the tutoring play?
Do you need help honing your skills in getting high scores?
Do you need help with the fundamentals of essay writing?
Do you need someone to help you deconstruct the main ideas and themes?
Do you need someone to help motivate you or guide you to study?
Your answer to each of the above will certainly give you a bigger picture about what you need. If you ask potential tutors how they can help you achieve your goals then it's more likely that you get a good tutor.