There is the ship-owner, larger and stronger than everyone on the ship, but somewhat deaf and rather short-sighted, with a knowledge of sailing to match his eyesight.  The sailors are quarreling among themselves over captaincy of the ship,  each one thinking that he ought to be captain,  though he has never learn that skill… On top of which they say it can’t be taught. In fact,  they’re prepared to cut to pieces anyone who says it can…. They beg him [the ship-owner] and do everything they can to make him hand over the tiller to them. [6*] Sometimes, if other people can persuade him and they can’t, they kill those others or throw them overboard.  Then they immobilize their worthy ship-owner with drugs or drinks or by some other means, and take control of the ship, helping themselves to what it is carrying.  Drinking and feasting they sail in the way you expect people like that to sail...  If someone is good at finding them ways of persuading or compelling the ship-owner to let them take control,  they call him a real seaman, a real captain, and say he really knows about ships. [Numbers added to facilitate exposition.]—Republic, 488a-d, translated by G. Ferrari.
There are at least ten criticisms of direct democracy in the famous comparison of the role of philosophy in a popular democracy to the captaining of a ship. Before I get to to those, in his notes, Ferrari suggests that 'the people' are likened to the ship-owner. This makes initial sense because they are, in some sense, the largest and strongest group. But I think it is more likely that this refers to the propertied classes (or gentlemen); after all, (a) the property of the shipowner is emphasized throughout the analogy, and (b) that the property can be seized by the masses. Even if (c) one reads the worthy (γενναῖος) as ironical, it makes more sense as a reference to the propertied than the people. This has additional benefit of making clear what I think of a more subtle point of Plato's: that a democracy also stultifies the propertied--they grow attached to goods not truth/virtue.
Okay, I think we can we summarize the ten criticisms as follows:
- Democracy generates dissensus.
- Self-rule generates overconfidence in each of us.
- The members of the demos lack [distinctive] political expertise.
- The people* deny the very existence of [distinctive] political expertise.
- The masses threaten or kill anybody who claims intellectual superiority.
- Everybody (is encouraged to) want(s) to rule. --> [6*] This can generate murderous conflict.
- The lower classes foment revolutions and steal property of others.
- With the people in control there is much rudderless pleasure.
- The majority are susceptible to flattery and demagogues.
- The masses call demagogues 'skilled.'
This calls for some comment.
On  that direct democracy generates dissensus is so because everybody can have a say and be in control and (so?)  everyone, who will have different views, wants to be in control. While there is an important point lurking here -- that people adjust their desires to what's possible --, as stated this is implausible. But all Socrates needs for the analogy to work is that sufficient people want to be in control. And that seems more plausible. It's interesting that Plato thought that the practice of direct democracy revealed the fact of pluralism. (Max Weber thinks this is a product of modernity and advanced division of labor.) In Plato this pluralism seems to be the product of the diversity and inconstancy of human desire/appetite [see 8] as such and the lack of regulation of these in a commercial democracy such as Athens.
On  that self-rule generates overconfidence in each of us is probably too strong. There are risk averse people. But that ruling, without external constraint (other states' power, etc.) creates overconfidence in some sense is not altogether implausible. Plato would have been able to point to the disastrous expedition to Syracuse as evidence.
Let's spot Socrates 3-4 for the sake of argument (although I return to these below). Obviously a friend of direct democracy or sortition would think this question-begging. (That's why I added 'distinctive.') On  Plato could fairly point to the trial of Socrates. Friends of direct democracy might argue (a la I.F. Stone) that the case of Socrates was the exception rather than the rule. On [6* & 7] much of the history of Greece as relayed by Herodotus and, especially, the (aristocratic-leaning) Thucydides, suggests an eternal return of local civil wars among the rich and poor. Interestingly enough, Athens seems to have been the relatively stable exception (presumably because the poor were subsidized by income from imperial tributes).+
In recent times, Plato's observations on [9-10] seem most prescient and relevant again. (Ahead of Trump's election, Jason Stanley drew on Madison and Plato -- but from Book VIII -- when describing the dangers of demagogues in the NYT; recall my responses here and here.]) The implications of  are the most interesting. Because while the core idea seems to be that the many deny the very existence of expertise in statesmanship [3-4], a demagogue can persuade them that a kind of ersatz-political craft is, in fact, the real thing. And while the rejection of expertise is bad enough, the embrace of fake-skill as the real thing corrupts -- presumably by undermining trust and by generating confusion about what it is. -- the very idea of expertise.
That is, the true skill of a demagogue consists in overturning pre-existing opinions. And this also points to the demagogue's true danger: he undermines the habits of thoughts and reasonable expectations for the worse (by [recall]) making everybody complicit in a reign of falsity. Okay, with that in mind let me sum up by way of a new presentation of [1-10]:
-  Direct democracy = dissensus [disorder/disunity].
-  Democracy generates overconfidence in each of us [reign of false].
-  The people lack of expertise [reign of false].
-  deny the very existence of political expertise [reign of false].
-  They threaten or kill anybody who claims intellectual superiority [disorder/anarchy].
-  Everybody wants to rule [disorder].
-  The masses ferment revolutions and steal property of others [disorder].
-  With the masses in control there is much rudderless pleasure [disorder].
-  The masses are susceptible to flattery and demagogues [reign of false].
-  The masses call demagogues ‘skilled’ [reign of false].
If we abstract from the details, all of Socrates's criticisms of direct democracy in the ship of state analogy can, then, be boiled down to two: (i) it generates disorder/disunity and (ii) a reign of the false (that is, lack of virtue). (Maybe that's too reductionistic; [5-6] both also predict murder and theft and these are, presumably, also bad simpliciter.)
So, first, in the ship of state analogy, Socrates presupposes some empirical facts about moral psychology of populations in and the normal functioning of direct democracy. And, second, Socrates also presupposes that (i) order/unity and a (ii) reign of truth are proper ends of statecraft.** Obviously, much of the Republic is devoted to arguing for these presuppositions and this post is not the place to scrutinize them.
The pressing question is how much the distinctive institutions of modern liberal democracy -- separation of powers, representative democracy, disestablishment of religion, wider franchise, the establishment of compulsory mass education, the abolition of slavery -- address Plato's challenge, or have made matters worse.