Where does a "High Priest" fall within the hierarchy of the Mormon Church?
The Mormon priesthood is divided into two "branches" for lack of a better term. The first, which is considered the "lower" or "temporal" branch is the Aaronic Priesthood, so named after Aaron, the brother of Moses, who was placed in charge of the temporal concerns of the people. The higher or more "spiritual" priesthood is called the Melchizedek Priesthood, called after the name of the ancient High Priest of Salem to whom Abraham paid tithes according to the Bible.
Within the Melchizedek Priesthood, there are three offices, the highest being "High Priest". The office of High Priest, is required to serve in virtually every leadership position of the Mormon Church from the organized congregational level and higher. Even the president of the Church, who is sustained as a prophet, seer, and revelator, is a High Priest. Mitt Romney, who served as a Regional Church leader is a High Priest. I served as a Counselor in two Bishoprics, which is a more local or less important, if you will, calling for a High Priest.
For those who are interested in knowing whether or not I was a high official in the Mormon Church, the simple answer is, no, not really. A Bishopric Counselor enjoys a certain amount of respect at the congregational level. Not much beyond that. I also served as one of seven presidents in a "Stake" (or regional) mission presidency. Some might argue that calling is a little more prestigious than that of a Bishopric Counselor. I'm not sure I would agree with that.
In the end of the day, I'm not looking for any deference on the basis of the prestige of my former Mormon positions in the priesthood. Both I, and you, and, I think, the average high school student, are all amply qualified to recognize the doctrinal inconsistencies that gave rise to my apostasy, once they are explained and understood.
See also -- Where do you stand on Mitt Romney's campaign?