  We show that central extensions of the mapping class group $M_g$ of the
closed orientable surface of genus $g$ by $\Z$ are residually finite. Further
we give rough estimates of the largest $N=N_g$ such that homomorphisms from
$M_g$ to SU(N) have finite image. In particular, homomorphisms of $M_g$ into
$SL([\sqrt{g+1}],\C)$ have finite image. Both results come from properties of
quantum representations of mapping class groups.
