If you are using Depth Map Shadows then I think that you need to turn up the Bias in the lighting options to around .9 and go from there. Raytracing shadows should need ammended and should appear correctly aslong as the penumbra is correct to give a soft edge.

Also as Alan stated change your options in the Renderer of your choice and turn on raytracing id your using that option and play with it from there. Rendering and lighting are all about tweaking and rendering and tweaking and rendering and tweaking...

It goes on... Enjoy