Easy) Assume Heisenberg's Uncertainty Principle is right, then what the demon knows, the precise location and direction of every molecule in both chambers, is impossible to have, so the problem can not exist. This is no criticism of Maxwell, who predates Maxwell.
Easy) The demon's knowledge is infinite information, and therefore impossible to have in a closed box.
2nd) Entropy is the loss of information, which the 2nd law of thermodynamics says can't happen in the box(closed system). The extra information must come from the new locations/direction of all the molecules that the demon is keeping track of.