  We consider the forced mean curvature flow in 2-d, finite range of dependence
and positive random forcing. We prove flatness and existence of effective speed
for initially flat propagating fronts. This is the analogue, in random media,
of a result of Caffarelli and Monneau. The main new tools are a large scale
Lipschitz estimate for the arrival time function, and a quantitative uniqueness
result which does not use uniform local regularity.
