I wrote "there's no evidence that space is quantized" and people have been
wondering why I didn't say "space is not quantized."
Answer: In principle, it might be quantized at some ridiculously small
scale, such as 10^-999 meters. Dynamics in such a lattice would be
indistinguishable from dynamics in a continuum. We see an analogous effect
in crystals, where electrons near the bottom of a band act like free
particles (with some effective mass). At higher energy, one sees
anharmonicity, band gaps, et cetera. If our universe has such
anharmonicities and band gaps, they are at such high energies that we
cannot detect them.
Bottom line: it is safe to _assume_ we live in a continuum, but it is
impossible to _prove_ it.