This is an old question, but I assume we’re going by StackOverflow rules here, so I guess it never hurts to update an old question with newer information.
As of 4.5, dynamic shadows are supported on mobile platforms with movable lights to a maximum of 2 cascades. I’ve also tested this with stationary lights, but currently it doesn’t seem to handle per-object shadows or directional dynamic shadows.
However, I believe the black objects shown in this screenshot were caused by a different problem. Mobile platforms seem to require a lighting importance volume around your map in order for movable objects to accept lighting.