Yes, I'm not getting unwanted artifacts anymore. But I have another question, take a look at this screenshot: http://s16.postimg.org/rzbnd4rv9/ss14538.png Is it normal that point light shadow is brighter than directional light shadow?
To this question and your original post. Shadows are the lack of light received. Most people think doing phong shading and then multiplying shadows works. The shadows as pointed out should be multiplied by the N*L diffuse calculation because it is basically saying "Is the surfacing facing the light: (yes then it is receiving photons)" "If it is facing the light, is something blocking it: (If so, then it receives no photons)". So if you perform all your lighting equation and texture lookups as if all the photons in the world hit it, it will get lit, and then some random multiplication happens to "darken" the image. It should be darkened by the fact that no light was hitting it in the lighting equation.
So this leads to your second question. Light is addative, without light every area in the world is completely black. So if your sun hits any surfaces not in shadow, those will be added quite highly with lighting (lots of photons hitting the surface). Then for every other light, more photons will hit.
So you have areas with:
Sun + Point light (which you can see very whitely)
Sun only (which is your brighter shadow because it received quite a lot of photons, just not the extra from the point light)
Point Light Only( this is your dark shadow. Only a few photons from the point light hit the surface, so its still pretty dark)