The format of the work is interesting, though. Two of the sections (II and IV) explicitly end with a prompt ("What do you think?" and "What do you think about this?"), suggesting that what we have here is something like prompts to get students thinking about certain subjects. Indeed, you could take any of the four sections and easily use them in a modern philosophy course as an essay prompt or a class discussion prompt. So Demodocus might possibly represent a way in which teaching was done in Plato's Academy, or in which philosophical teaching more broadly was influenced by the Platonic dialogue genre.
(in order of appearance)
Demodocus is presumably the same as the Demodocus in the Theages there he talks with Socrates about the education of his son Theages. (In passing Demodocus and Theages happen to mention the topic of advice, which is the topic of Section I.) Theages himself is mentioned in passing in the Republic and the Apology (and Demodocus in the latter), but not much is known about either him or his father. Demodocus never speaks in this dialogue; he is addressed, and so is present, but we hear nothing from him.
Each section of the dialogue is first person. The narrator is never named, and may or may not be Socrates.
I. Section I is a monologue in which the narrator addresses Demodocus, who has asked him to give advice on matters that will be discussed in a meeting. The narrator says that he would prefer "to ask what is the point of your assembly and of the readiness of those who think to give you advice and of the vote which each of you intends to cast", and this gives the structure of the section: the narrator questions why the assembly would be asking advice, then why anyone would consider himself ready to advise the assembly, then why voting would be considered useful. The narrator ends with making a distinction between two kinds of topic on which one might give advice.
II, III, & IV. The next three sections each have the narrator describing in third person an argument between two people (different pairs of people for each section). In Section II we have a man rebuking a friend for believing the plaintiff in a case when he had not heard the defendant's story. They both discuss the proverb that you should never judge a case until you have heard both sides of the story, and the narrator ends perplexed about the question, asking the reader for help. In Section III we have someone criticizing a person for not trusting him enough to lend him money, and his interlocutor asks why he is criticizing someone for not being persuaded while refusing to criticize himself for failing to persuade. In Section IV someone is criticizing another for trusting strangers too easily, and his interlocutor argues that this criticism does not make sense. It then ends with the narrator admitting perplexity again and asking the reader about it.
I. The argument of Section I has some affinities to that of Sisyphus. If it's impossible to give good and informed advice, it would be silly to ask someone to advise you. But what makes for good and informed advice? It seems that the adviser must have knowledge. If the assembly that's asking for advice, however, has that knowledge, it does not need the advice. But if the assembly doesn't have the knowledge, how can it discuss the topic? Moreover, the assembly asks advice from several people; but if one person has the knowledge to give good and informed advice, then that advice seems to be adequate, since good and informed advisers would give the same advice. So by asking for advice, the assembly is assuming that advisers have knowledge; whereas by asking several people, it is assuming that they don't.
The narrator then looks at it from the adviser's side. If there are several advisers, suppose they give different advice; then how could they all be giving good, informed advice? But if they give the same advice, why do they all need to be giving advice? So these are ways that the adviser's readiness to give advice. (Note, incidentally, that one case is not discussed, namely, of the single adviser who is genuinely informed. This is important.)
The next point has to do with the point of voting. It seems that it's a way of judging the people who give advice. But if the assembly knows enough to judge this, they don't need the advice. On the other hand, if they don't have the adviser's knowledge, they are not competent to judge the advice. The assembly cannot make itself competent to judge the advice. Nor can the adviser be claiming also to teach the assembly how to judge the advice, because people are only given a little time to advise assemblies and there are so many people in an assembly. So there is no point in voting:
Surely your meeting is inconsistent with your voting and your voting with the readiness of your advisers? For your meeting implies that you are not competent but need advisors, while the casting of votes implies that you do not need advisers but are capable of judging of giving advice. And the readiness of your advisers implies that they have knowledge, while your casting votes implies that the advisers do not have knowledge. (382b)
Further, even if the assembly implements a plan, it does not know whether the plan will fulfill the goal, nor does it know if the goal is really in its best interest, nor does it seem that anyone knows anything about these kinds of things. This means uncertainty and indecision. But this contrasts with what a good person would do: a good person would have knowledge of the things on which he advises, and those whom they persuade will attain good as their goal, and having good they will not have to change their minds.
There's more to this argument than seems to be happening on the surface, which is why I've given some detail in my summary here. Superficially it looks very skeptical, but the author is making a point quite similar to points made in Gorgias about practicing true politics, and how it cannot be done en masse but only one on one, and it must be based on knowledge of the good rather than persuasion, and it cannot be decided by general vote.
II. Why do we think you can't judge a matter fairly before you've heard both sides of the question? If you can't tell whether one person is speaking the truth, then it seems you can't tell which of two people are speaking the truth, and if one person is not clear enough, it doesn't seem that you can make it clear by adding another person when one of the two, one does not know beforehand which, is speaking falsely. Further, you can only hear them one at a time. But if you hear the first person and that's enough to clear it up, you don't need the second person's testimony.
III. Why do we criticize people for not trusting us? It seems we should criticize ourselves. First, because if they didn't trust us, they succeeded at getting what they want, but we failed at getting what we wanted, so we did something wrong. Second, if we asked for something they shouldn't have given us, they did what was right and we did something wrong. If, on the other hand, we asked for something that should have given to us, we failed, and did something wrong. Third, if they didn't trust us, we failed to persuade them; so we did something wrong. So we should be criticizing ourselves if others don't trust us.
IV. Why do we think it is more reasonable to be quick in trusting family and friends than in quickly trusting strangers? If we're quick to trust people who tell the truth, that's not a bad thing, whomever they may be. If we are slow to trust someone, and then eventually are persuaded, and turn out to be deceived, that doesn't seem a better thing. When we criticize people on this point, we criticize them for trusting those who are not trustworthy. To do this, if they are strangers, he needs to consider whether they tell the truth. But the same is true if they are family and friends. Further, whether one is trustworthy does not depend on whether one is a friend or a member of a family, because everyone is friend to someone or family to someone.
These four sections involve a somewhat tighter structure than I think they're usually given credit for. The first two sections both deal with persuasion in public settings (assembly and trial), and the second two both deal with trust. In fact, all of the sections are concerned with the problem of trust and persuasion, and they all indicate problems with how we typically understand these -- in particular, the same problem, that we do not actually treat truth as the real foundation of trust and knowledge or education as superior to persuasion. But the dialogue explicitly leaves it up to the reader to start working out how the alternative would work.
Quotations from Jonathan Barnes's translation in Plato, Complete Works, Cooper and Hutchinson, trs., pp. 1699-1706.