There cannot be an unknown factor which renders a valid argument in valid. An argument makes explicit all of the propositions on which it rests. The propositions themselves are irrelevant to validity: a valid argument is true for all possible combinations of truth values of the propositions. It is valid in any imaginable universe, so to speak. That is to say, we can take all of its distinct propositions, replace them with unique variable names, and then evaluate it for all combination of truth values of those variables, and it must come out true.

If an argument is valid, then we can further consider whether it is sound: are its propositions true when interpreted in some relevant world (often the real one, but possibly any imaginary world that the debaters agree about, e.g. the Star Trek universe or whatever). Being valid, the argument will of course be true, but if it is unsound for the given world, it will only somehow be vacuously true in that world. For instance, by exhibiting a false conclusion from a false premise in a conditional.

Applying this reasoning rigidly to the examples presented in http://www.iep.utm.edu/gettier/ readily unravels their issues. For instance, the lucky coincidence that Smith has ten coins in his pocket readily succumbs to the fact that this situation isn't true in all imaginable universes; it is a separate proposition from "Jones has ten coins in his pocket". It gets a separate variable, and is separately considered both false and true when we go through all the possible variable values.