The idea seems to be that a collection of individuals, each of whom has some evaluative ability, may, as a group, have overall a greater evaluative competence than a single expert. (It is important to note that Aristotle is cautious and does not think this always happens. It just might happen sometimes.) So there is some notion of there being an additive quality of the relevant skill or character trait. Provided the individuals in the group are not entirely slavish then you can add them together and sum their respective competences. This seems odd just because it is not clear that virtue and wisdom (aretē and phronēsis: 1281b4–5) are the kinds of things that can be summed in this fashion according to Aristotle. Now it is possible to claim that what Aristotle means here is that collective decision-making by a group of individually deficient judges can be effective because the group itself generates a kind of helpful reflection: each learns from the others and overall a good decision is reached. Perhaps that is a plausible idea. 
Unfortunately, I am not sure this fits very well with the way the rest of the paragraph is presented and, in particular, the various analogies that are offered. Aristotle goes on to claim that a good person brings together in one individual the relevant skills and competences but these might be scattered and distributed between a number of individuals, each of whom is worse overall than the good person, but who when combined are better. This is not a mere additive notion since the idea here is that the group comes together as if to form a single agent (1281b5). This also seems to make better sense of the analogy of the feast at 1281b2–3: many people bring dishes to a meal. The feast is better than a single dish, even if that single dish is excellent while each of the many dishes in the feast is not as good as the single dish. This seems plausible to me only on the assumption that the group of many dishes (deipna) contains a variety of dishes and, what’s more, that variety is such that for example one is a starter, one a main course, one a dessert and they combine to make a feast (dapanē 1281b3). It is not obvious (though I can see how someone might want to argue for it) that a collection of a large number of mediocre but pleasant chocolate mousses is better than a single really excellent chocolate mousse. Certainly, I’m not at all convinced that the collection is better in terms of chocolate mousse-ness. But if each dish brings something different that contributes to the overall meal as a whole then perhaps the collection may be better than the single very good item taken on its own.
Incidentally, this notion of adding together complementary parts into a whole is probably present already at 1281b4–5 where the many individuals each have a ‘part’ (morion) of virtue. If we think of the parts not merely as ‘a certain quantity’ but rather as parts in the sense that each jigsaw piece is a part of the overall puzzle, then adding together all of these parts is what is needed for a good whole.
If that is right then thinking in terms of collective decision making that involves debate, reflection, learning from one another and so on, might be a more plausible way to defend the idea of the competence of crowds, but it doesn’t fit well with Aristotle’s analogies which are instead put in terms of this ’jigsaw pieces and jigsaw-puzzle’ model.
This idea of a sum of the good parts of a collection of different items, where each item is overall not that great, seems also to be what Aristotle has in mind in the analogy from aesthetic judgement at 1281b8–10: if each person makes a good judgement about a separate aspect of the performance (one is good at flute-playing evaluation, another at evaluating some part of the dancing) then they might add up to a single all-round excellent judge. It doesn’t matter that the good flute judge has no idea about choreography because it’s only the flute-judging jigsaw piece that he provides. Similarly, at the end of the paragraph Aristotle seems to have in mind that the collection is a collection of just those positive aspects of each of the individuals. He compares a single beautiful person with an combination of a set of different beautiful parts from different individuals: Clooney’s jawline, Grant’s eyes, etc. etc. (1281b12–15).
But that raises is another worry. It’s just not true that if you bung together a collection of the best bits of different faces the collection is going to be as good as if not better than a single beautiful face. Here’s the proof:
 I think this is the sort of view favoured in R. Kraut, Aristotle: Political Philosophy (Oxford, 2002), 402–6.