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Another reason omniscience is impossible is that knowledge is gained by a process, and no one can process everything. If we define infallibility as immunity from making mistakes, we have a different question from the one DavidOdden answered. I still think the answer is no, but I'm not ready right now to give a good explanation.

Omniscience is universally impossible in principle, insofar as the scope of “all” in all-knowing includes experiential knowledge of events that have not happened (you cannot experience a thing before it happens), or of events that preceded the existence of the particular consciousness. Infallibility on the other hand is meaningless (impossible for a different reason). I cannot hear microwave radiation, but that is not a failure, that is because of my nature (or, the nature of humans, or mammals). If you switch to omnipotence, that just leads to a different kind of incoherence. For example, humans can see light in a particular range, using their eyes, and can hear sound in a different range, with their ears. You can’t hear light or see sound, and you can’t digest light or sound either. Plants can “digest” light, but then we are metaphorically toying with the word digest. There are many things that humans are incapable of doing, including a whopping load of meaningless “things”. Omnipotence is also conceptually incoherent. Our solution to the problem of certainty is to understand what it is. Certainty is contextual – a proposition is certain if all actual evidence in a knowledge context points to the conclusion and alternatives are also disproven. Arbitrary uncertainty is a fiat declaration that “one can imagine”, that is, reifying imagination into being a “fact”.