  We consider stochastic partial differential equations under minimal
assumptions: the coefficients are merely bounded and measurable and satisfy the
stochastic parabolicity condition. In particular, the diffusion term is allowed
to be scaling-critical. We derive local supremum estimates with a stochastic
adaptation of De Giorgi's iteration and establish a weak Harnack inequality for
the solutions. The latter is then used to obtain pointwise almost sure
continuity.
