I think if the coarse moduli space is smooth, so is the DM stack, because XX --> X is a gerbe, which is always smooth (since smoothness can be checked fppf locally on X, and B(G/X) is smooth over X). A stack (or a morphism of stacks, not necessarily representable) is defined to be smooth if one can find a presentation which is smooth over the base. And if it is smooth, then any presentation is smooth. That's why I got confused on Anton's example. Maybe someone can explain this to me. Thanks in advance.