Having given this about ten seconds of thought, I would say that one usually cannot say that all the facts have been accounted for, except perhaps in cases of pure mathematics, i.e. 2 + 2 = 4, the sum of the internal angles of a traingle is 180 degress (in Euclidean geometry, of course), etc.
This is slightly out of my depth (by 'slightly,' I mean 'way'), but didn't Gödel show there could be cracks of doubt even in pure math?
From Boyer's History of Mathematics
'Gödel showed that within a rigidly logical system such as Russell and Whitehead had developed for arithmetic, propositions can be formulated that are undecidable or undemonstrable within the axioms of the system. That is, within the system, there exist certain clear-cut statements that can neither be proved or disproved. Hence one cannot, using the usual methods, be certain that the axioms of arithmetic will not lead to contradictions ... It appears to foredoom hope of mathematical certitude through use of the obvious methods. Perhaps doomed also, as a result, is the ideal of science - to devise a set of axioms from which all phenomena of the external world can be deduced.'
I see from Wikipedia that Gödel's first theorem is 'one of the most misunderstood,' and I'm probably proving them right. Any math people want to weigh in?