Given the shadow artifacts that are appearing on the front, top face of the cube, I think that you have a few areas that you should look at.
First, on the light itself, look at the various bias settings. Try first adjusting them until that is gone.
Next, head over to the player and quality settings. Try lowering your shadow distance there. Make it really low at first (like the distance between the plane and the camera). That should help a LOT with the artifacting that you are getting. Once you've done that, adjust it up until you have a comprise between smooth shadows and a good distance. It is usually default to a value that I've always found to be way too high.
Good luck! I think that both of those will take you a long way.