Answer to your question: Honestly, I should not have included that line about errors in there at all; it doesn't need to be special cased out because most errors are emergent. (Not always; a missing negative somewhere is not emergent. But when you get to the complexity of a video game, most errors that will make it through QA are emergent.)
But also: I actually have thought about this a bit since I wrote this, and I think I can come up with a decent general definition for emergence: (don't worry, I'll get to your question in a moment)
Something is emergent when it is caused by a rule that works similarly to the second law of thermodynamics. (More specifically, the property of the second law that it isn't actually a hard law at all; it's just that when you crunch all the probabilities for all the particles involved, it is vastly more likely that the result will obey the second law then will not.)
Similarly, the ways economies develop aren't hard laws; it would be entirely possible for an economy to develop in such a way that it lets you get a free lunch. It's just that that, considering all the actors involved are out to find and take those free lunches, that you are about (using about very broadly here) as likely to find an actual free lunch as you are to find your foot has suddenly turned into gold.
(Also: I think it's a mistake to point at some finished product of laws of emergence and say it's emergent. "The economy is emergent" is just a short and slightly misleading way to say "The laws that govern an economy are laws of emergence".)
But going back to what this predicts: It predicts mainly that there is something equivalent to atoms in thermodynamics or actors in economics; some small unit of behavior that you can test for. It also predicts (in very complex systems it might not be possible to do any actual math on this, but in theory it predicts) how often the law will fail. (As noted, sometimes all you can say with confidence is "it might fail sometime"; of course if it fails OFTEN it doesn't have enough predictive value to justify keeping around.)
The failures of phlogiston and vitalism are historical hindsight. Dare I step out on a limb, and name some current theory which I deem analogously flawed?
I name emergence or emergent phenomena—usually defined as the study of systems whose high-level behaviors arise or “emerge” from the interaction of many low-level elements. (Wikipedia: “The way complex systems and patterns arise out of a multiplicity of relatively simple interactions.”)
Taken literally, that description fits every phenomenon in our universe above the level of individual quarks, which is part of the problem. Imagine pointing to a market crash and saying “It’s not a quark!” Does that feel like an explanation? No? Then neither should saying “It’s an emergent phenomenon!”
It’s the noun “emergence” that I protest, rather than the verb “emerges from.” There’s nothing wrong with saying “X emerges from Y,” where Y is some specific, detailed model with internal moving parts. “Arises from” is another legitimate phrase that means exactly the same thing. Gravity arises from the curvature of spacetime, according to the specific mathematical model of General Relativity. Chemistry arises from interactions between atoms, according to the specific model of quantum electrodynamics.
Now suppose I should say that gravity depends on “arisence” or that chemistry is an “arising phenomenon,” and claim that as my explanation.
The phrase “emerges from” is acceptable, just like “arises from” or “is caused by” are acceptable, if the phrase precedes some specific model to be judged on its own merits.
However, this is not the way “emergence” is commonly used. “Emergence” is commonly used as an explanation in its own right.
I have lost track of how many times I have heard people say, “Intelligence is an emergent phenomenon!” as if that explained intelligence. This usage fits all the checklist items for a mysterious answer to a mysterious question. What do you know, after you have said that intelligence is “emergent”? You can make no new predictions. You do not know anything about the behavior of real-world minds that you did not know before. It feels like you believe a new fact, but you don’t anticipate any different outcomes. Your curiosity feels sated, but it has not been fed. The hypothesis has no moving parts—there’s no detailed internal model to manipulate. Those who proffer the hypothesis of “emergence” confess their ignorance of the internals, and take pride in it; they contrast the science of “emergence” to other sciences merely mundane.
And even after the answer of “Why? Emergence!” is given, the phenomenon is still a mystery and possesses the same sacred impenetrability it had at the start.
A fun exercise is to eliminate the adjective “emergent” from any sentence in which it appears, and see if the sentence says anything different:
Another fun exercise is to replace the word “emergent” with the old word, the explanation that people had to use before emergence was invented:
Does not each statement convey exactly the same amount of knowledge about the phenomenon’s behavior? Does not each hypothesis fit exactly the same set of outcomes?
“Emergence” has become very popular, just as saying “magic” used to be very popular. “Emergence” has the same deep appeal to human psychology, for the same reason. “Emergence” is such a wonderfully easy explanation, and it feels good to say it; it gives you a sacred mystery to worship. Emergence is popular because it is the junk food of curiosity. You can explain anything using emergence, and so people do just that; for it feels so wonderful to explain things.
Humans are still humans, even if they’ve taken a few science classes in college. Once they find a way to escape the shackles of settled science, they get up to the same shenanigans as their ancestors—dressed up in the literary genre of “science,” but humans are still humans, and human psychology is still human psychology.