Here goes:
Quite how much we should value consistency is an interesting issue.
I have looked up all meaning of "quite", but still puzzled by that.
In your example, quite is synonymous to exactly.
"Exactly how much we should value consistency is an interesting issue."
"He is not quite capable of the task"
He may be capable, yes. But not as much as we would like him to be for completing this task. Not quite capable.
"He is quite capable of the task"
He is very capable of this task. Even more capable than required for completing this task.
"I am quite sure, that he is capable."
I am very sure, that he is capable.
"I am not quite sure, that he is capable."
"I am not so sure, whether he is capable or not. Maybe he is but I am doubt."
"They told me that I was quite mistaken"
They told me that I was very mistaken
"I did not quite see what happened"
"I did not exactly see what happened"