If Father Christmas behaves as a quantum entity (a santon, presumably with very large charm and quantum numbers), physics allows him to pass through many orifices (chimneys) at the same time.
This is possible as long as no experiment is set up to observe him passing through any particular chimney (otherwise his wave function collapses and you end up with reindeer all over the place).
All children are told that they must never attempt to detect santons, so the success of the scheme is a great tribute to the obedience of the children of the world; for this to work they must all be good.
After Father Christmas has passed through all the chimneys at once it is permissible to detect the santon field on a suitable detector. It would seem that santons are detected by pine trees and stockings, which register the collapse of the santon field as small piles of presents. The fact that presents never appear in stockings already occupied by a foot may be a consequence of the Pauli Exclusion Principle.
Thus Father Christmas can visit all the children in the world at the same time and can continue to do so as long as we never attempt to observe him passing through a particular chimney. I strongly suggest that funding for experiments to do this should be withheld as success would mean no presents.