  We report results of large-scale Monte Carlo simulations of
superfluid--insulator transitions in commensurate 2D bosonic systems. In the
case of off-diagonal disorder (quantum percolation), we find that the
transition is to a gapless incompressible insulator, and its dynamical critical
exponent is $z=1.65 \pm 0.2$. In the case of diagonal disorder, we prove the
conjecture that rare statistical fluctuations are inseparable from critical
fluctuations on the largest scales and ultimately result in the crossover to
the generic universality class (apparently with $z=2$). However, even at strong
disorder, the universal behavior sets in only at very large space-time
distances. This explains why previous studies of smaller clusters mimicked a
direct superfluid--Mott-insulator transition.
