Being a hitting coach myself, I'm a bit biased, but I'll do my best to answer.
Jerry said it best when he said "The job of a good hitting coach is to eliminate his job. The key is to to teach the hitters how to coach themselves." That's absolutely right, and any coach worth his salt is going to go into his job with this goal in mind. He wants the student to succeed without his help - not only for the personal satisfaction, but because that student will give glowing reviews of the coach to his peers!
Good coaches explain things in terms the student can understand. The coach will never rush things or force his ideas on the hitter - instead, he will adapt what he knows to suit the hitter's personality and approach as best as possible.
A good hitting coach will have at least 30 FPS video of the hitter from the side and from the front, and be able to point out both his flaws and his strong points in a way that is constructive to the student. If the coach does not use video, he is 99% of the time going to be ineffective or even counterproductive.
Good hitting coaches will prepare the hitter for a game situation by getting him live pitchers to hit off of. He will not simply have him hit off a tee or soft toss alone, though both are very useful in developing the swing. Without seeing a significant amount of live pitching, there is no way the lessons can be totally effective.