ReasonFirst

ReasonFirst,
Descartes thought the only reason we humans err is that we let our will outrun our understanding. He and many others thought that God could not err. That was because they thought error would be an imperfection. That is foolishness, I say. Where there is no error, there is no intelligence. God was traditionally thought of as having a will (there was the choice to make the world and to make humans) and as having understanding, or intellect. Although Descartes would emphasize the extent of the divine will, whereas Leibniz would emphasize the extent of the divine understanding, all could agree that for God, Its will cannot outrun Its understanding. Its understanding, Its intellect, may be pure act, but it is not a process requiring time to obtain knowledge. This idea of divine infallibility (and omniscience) in comparison to human fallibility (and partial ignorance) might be thought analogous to a real refrigerator and a perfect refrigerator, as in thermodynamics. The Second Law says the perfect refrigerator can be compared to real refrigerators, but no real ones can attain coincidence with the perfect one. I think that analogy would be an inappropriate analogy. Although we can get better at avoiding errors (and I would say that the best outside help on that is elementary logic texts which include informal fallacies as well as formal ones; the former can be supplemented by the informal fallacies Rand formulated, or anyway rediscovered and renamed, such as the Stolen Concept Fallacy |—>The Art of Reasoning), we would rationally expect to make errors even when proceeding with the greatest care and conformance to logic. We must not suppose it is possible to make no innocent errors, even as we get more skilled in avoiding them and even with the self-correcting methods of the hard sciences. That would be an error. For comparisons of human intelligence with other intelligence, I should suggest comparison of our cognition with the cognitive powers of the great apes, and not with imagined chimera such as God.
A Natural History of Human Thinking
 

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”.

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.
 

Sure, they could be mistaken but the issue is why are they so confident in their knowledge. If it's about the high stakes, meaning, "I can't afford to be wrong", then the heightened emotions are causing the irrationality. At that point anything goes, and if you have confidence in them, then you are in trouble. Otherwise, if they know they are being arbitrary, I don't know what the motive would be, other than maybe they want to hurt you/misguide you.

Similar to the question of God, what created God. What matrix created the matrix we are in, going on infinitely. Or maybe there are Gods instead of on God. So maybe there are multiple matrix's. In other words, what if this matrix is in a matrix itself, and that one in another one. What if we are in a matrix that is part of a dream? What if we are in a matrix that coexists with another one ... and on and on with the possibilities.
That is the problem with "arbitrary", it is eternally undeterminable.
Kind of like x/0, a divide by zero problem is undeterminable with infinite possibilities. Maybe it's 8, maybe its 52 because both multiplied with zero are zero. They are all possible. You don't know which number it is, but you know that you can never determine it. In fact one knows that is eternally undeterminable.
One thing I notice is that there are two interpretations of the matrix issue
1. The matrix is a simulation in this world. Meaning, you may be mistaken about your location. you are not where you think you are.
2. The matrix is a way of saying there is no reality. There is no real world. kind of like existence does not exists. It falls apart because the matrix requires existence, for itself to exist.
#1  is an empirical question, requiring experimentation and trial and error to see if there is any evidence and to "find" the actual room that you are in. It is not a refutation of existence, just an assertion of an error. In that case, it is not an attack on epistemology. 
Since you think an attack on epistemology is involved, you would be arguing the second definition of the Matrix. That maybe existence does not exist. In that case, that matrix does not exist, period!