The LDS church claims that on 15 May 1829, John the Baptist conferred the Aaronic Priesthood on Joseph Smith and Oliver Cowdery. Section 13 of D&C is cited as evidence, but this section was not in the original Book of Commandments.
They claim the Melchizedek Priesthood was organized by Peter, James and John, but no date is given. It is absent from the original Book Of Commandments. Joseph Smith said, concerning a conference in 1831, "...the authority of the Melchizedek Priesthood was manifested and conferred for the first time upon several of the elders." This is in History of the Church, Vol. 1, pp. 175-176
Supposedly the Melchizedek priesthood was bestowed on Smith and Cowdery by the apostles Peter, James and John. Mormons say that you must hold the Aaronic priesthood before you can hold the Melchizedek priesthood, yet the three cited apostles were definitely never Levitical priests! And we know Melchizedek didn't hold the Levitical priesthood!
The O.T. clearly says that only direct descendants of the tribe of Levi can hold the priesthood (Ex. 28:1, Num. 18:1-7, Lev. 6:19-23, Nehemiah 7:61-65). Most Mormons, including Joseph Smith, claim to be from the house of Ephraim. Ephraim had no right to the priesthood, which would mean most LDS men would be cursed if they tried to usurp the priesthood (Num. 16:1-3, 21 and 1 Kings 13:33-34). Additionally, to be ordained as a Levitical priest, there were certain rituals required that LDS does not perform (Ex. 29:4-27). The need for a Levitical priest was done away with when the temple veil was rent at Jesus' crucifixion.
The Melchizedek priesthood was a priesthood of ONE. It existed before the law was given (Gen.14:18) and after the law ended (Heb.7:11-17). Jesus became that one high priest that presented the final sacrifice, negating the need for further temple priests. At any rate, no where in scripture do dead priests come back to confer the priesthood on another.
As I noted in my article on Melchizedek (http://tinyurl.com/melchizedek), The law of Moses and the priesthood went together. All the people without exception were sinners, subject to the law's condemnation, and were thus in need of a priestly system to mediate between them and God. The Aaronic priesthood was imperfect, but the Melchizedek priesthood was perfect (as implied in Hebrews 7). The announcement of the coming one who would be a priest forever (Ps.110:4) was written midway in the history of the Levitical priest-hood, which could only mean that the existing system was to give way to something better. Jesus came from the non-priestly tribe of Judah, but became a priest forever in the Melchizedek order. There is no indication in the scripture that any other person held this high priesthood.
The Mormon priesthood is a fraud.