Alma 13:1-5/Authority of high priest
The discussion of the priesthood in verses 1-20 may be read as Alma providing support for his authority as a high priest to call the people to repentance. Note how explicitly Alma does this in, for example, Alma 13:21.
To place this support for Alma's authority in context, note that the invitation to repent (see Alma 12:37) comes as a sort of repetition of a more originary invitation to repent, the one issued to Adam and Eve when they were first visited by angels outside the Garden of Eden: "But God did call on men,... saying: If ye will repent, and harden not your hearts, then I will have mercy upon you, through mine Only Begotten Son;... these shall enter into my rest" (Alma 12:33-34). Alma calls these words to Adam and Eve the "second commandments" (Alma 12:37; the "second commandments" are opposed to the "first commandments" of Alma 12:31, which concerned the eating of the fruit in the Garden of Eden). It is to these "second commandments" that Alma refers in the first verse of chapter 13: "I would cite your minds forward to the time when the Lord God gave these commandments unto his children...." Since it was apparently at the time "these commandments" were given to Adam and Eve that "the Lord God ordained priests, after his holy order, which was after the order of his Son, to teach these things unto the people" (also in verse 1), the move from the "second commandments" (the invitation to repent) to the ordination of priests is not strange or shocking: Alma, as one who has been ordained "to teach these things unto the people" is clarifying his role in the Adamic story he has just told at the conclusion of chapter 12 (having received the command to repent, and having repented, Alma is assigned to teach others, as he is presently doing).
Perhaps what suggests the incoherence of Alma 13:1-20 is not the transition at its beginning, however, so much as its re-transition to repentance at its end. However, even this seems to be explained by the above comments: having established at length (twenty verses' length) his own role as authorized preacher, Alma returns to the exhortation. The passage is entirely coherent in its context. It is, in fact, entirely coherent according to the first suggestion made above: Alma sees some necessity to ground his authority to preach before confirming his call to repentance. What remains to be discussed, then, is why Alma feels the need to establish so carefully his authority to preach.
Perhaps the answer to this goes back to several far earlier moments in the situation at Ammonihah. In Alma 9:6, after Alma's first words of discourse (after, of course, his return), the people of Ammonihah respond by calling his authority into question: "And they said: Who is God, that sendeth no more authority than one man among this people, to declare unto them the truth of such great and marvelous things?" When this question of authority is put to rest by Amulek's second witness, Zeezrom raises a more subtle question concerning Amulek's (and perhaps by extension, Alma's) authority. In Alma 11:32-37, Zeezrom questions Amulek about Christ's coming and the salvation He will bring. When Amulek responds, Zeezrom warns the people that Amulek speaks "as though he had authority to command God." One reading of Zeezrom's logic runs as follows: one cannot say (predict, prophesy) what another "shall" do, unless the one saying (predicting, prophesying) is in a position to dictate the other about whom he or she speaks--unless, in other words, the one saying has authority over the other. In short, Zeezrom suggests--in a locution not unlike some made today--that a "prophet" (or at least one who speaks the future of God) can only be such by subjecting God to him- or herself. This amounts, on Zeezrom's part, to a wholesale rejection of any claim to religious authority (a priori). (It should be noted that this is only one possible reading of Zeezrom's point concerning authority.)
It may be that Alma sees fit to take up the theme of priesthood (as authorization to preach of a coming Christ) to respond to these two accusations against the authority of Alma and Amulek. Though Amulek's mere presence calls the first accusation into question and Amulek's clarification (in Alma 11:36-37) seems summarily to do away with the second accusation, Alma's twenty-verse excursus on ordination may be read as a careful, detailed response to these two questions of authority. Throughout the passage, Alma makes constant reference to "they" and carefully doubles Melchizedek with reference to Abraham, perhaps to emphasize the fact that God does send more authority than one man. Moreover--and more interesting--Alma describes the ordination itself as pointing forward to future events, apparently thereby allowing the ordained to know of things to come (see especially verse 2: "those priests were ordained after the order of his Son, in a manner that thereby the people might know in what manner to look forward to his Son for redemption").