Does the Planck scale imply that spacetime is discrete?

On a quantum scale the smallest unit is the Planck scale, which is a discrete measure. There several question that come to mind: Does that mean that particles can only live in a discrete grid-like structure, i.e. have to "magically" jump from one pocket to the next? But where are they in between? Does that even give rise to the old paradox that movement as such is impossible (e.g. Zeno's paradox )? Does the same hold true for time (i.e. that it is discrete) - with all the ensuing paradoxes? Mathematically does it mean that you have to use difference equations instead of differential equations? (And sums instead of integrals?) From the point of view of the space metric do you have to use a discrete metric (e.g. the Manhattan metric ) instead of good old Pythagoras? Thank you for giving me some answers and/or references where I can turn to. Update: I just saw this call for papers - it seems to be quite a topic after all: Is Reality Digital or Analog? FQXi Essay Contest, 2011. Call for papers (at Wayback Machine), All essays, Winners. One can find some pretty amazing papers over there.