The absence of evidence is not the evidence of absence. Just because we have an instance of conscious thought leading to the conclusion, and a scenario where it is possible that the unconscious is playing a role, the conclusion that in the second scenario the unconscious does not play a role based on the ability to come to the conclusion consciously does not follow. The nature of the problem here is not given enough of a definition for one to conclude that there is only one way to get to the answer, either.
>"The brain’s networks of neurons are highly interconnected, so there seems little scope for assigning different problems to different brain networks."
Except we know very well that the brain solves different kinds of problems in different areas... the Occipital lobe, Wernicke's area vs Broca's area, are different "sub problems" the brain is working on which the conscious part gets information about. Maybe different creative problems use the whole frontal cortex differently, but the "computational machine" that is our brain is definitely divided up into sub-problems; some are very, very obviously unconscious, like the "problem" of keeping our hearts beating.
>" If it is indeed possible to search for foods or countries simultaneously (even though we can consciously report the results of only one search at a time), then the rate at which we generate answers in both categories should be substantially greater than the rate at which we can generate answers from either category alone."
I think this is a bad experiment and a bad conclusion. It's a bad experiment because in the "control case" (only listing foods or only listing countries), the unconscious, if helping, would still be helping in these cases, trying to generate a list while the conscious mind is also trying to generate a list. So it's not really a controlled experiment, because the unconscious mind is never "stopped" - it is assumed to not be used. It's a bad conclusion then because the premise is faulty; we wouldn't expect someone to list two separate lists more quickly if the same unconscious mechanism is a poor assistant when making the lists alone, too.