I agree with Longtoss. For us, the key is reaching a place where my son is able to recognize what might be going wrong in his swing and make corrections. It takes a while to get to that point. And, I agree that each teacher will have different ideas. I think it is important to realize that even small adjustments to a hitter's swing take much repetition (muscle memory thing). Obviously, terminology is important as well -- and a single instructor can establish consistency in that area.
I think I see where you're going ctiger --- what about these guys that spend $$$alot$$$ on private instruction, then stand in front of their HS coaches with "flaws"? In that case, a player should be able to describe his approach (which hopefully echoes that of his private instructor)....that way, the two coaches need not reinvent the wheel.
We have not invested years in private instruction, but have found an instructor that is a good communicator.
ct -- regarding your comment about making a kid "feel good" about his swing....I think that is important as well, as long as it is sound. As you know, hitting is 40% physical and 75% mental.