The H-T phase diagram of two-dimensional amorphous MoGe superconductor
s is studied near H(c2) and near the melting line of the vortex lattic
e. Good agreement with the lowest Landau level approximation is found
for the broadening of the specific heat in a field. We also find that
melting of the vortex lattice can be observed only on short enough len
gth scales, shorter than the disorder-mediated lattice correlation len
gth.