This issue looks like standard shadow map acne artifacts. Additionally your's lighting equation is incomplete or wrong. Light shouldn't influence faces with normals facing away from it. This also means that with a proper equation the "dark" side of the sphere shouldn't have any acne artifacts.
There are three sources of acne artifacts:
- First acne source is shadow map precision. Make sure that near and far planes of shadow casting light are as tight as possible. All objects before the near plane can be pancaked, as their exact depth isn't important.
- Second acne source is shadow map resolution. For a directional light you should be doing cascaded shadow maps with at least 3 1024x1012 cascades for ~100-200m of shadow distance. It's hard to cover similar shadow distance with one shadow map with uniform projection.
- Third acne source is wide shadow map filter like PCF, as using a single depth depth comparison value across a wide kernel is insufficient. There are many methods to fix it, but none of them is robust.
To sum up, a tight frustum with a few cascades and some bias tweaking is enough to get the general case working (directional light). Start tweaking by disabling shadow filtering and tweak for filtering only when basic shadow maps are robust enough.
Additionally apart from the constant depth bias (which you currently use) you should also add slope depth bias and max slope depth bias. Both can be be implemented either as render state or as shader code during shadowmap rendering. Slope depth bias is simply a magic bias value scaled by dot( normal, lightDir ).
There are some additional interesting methods and most of them are implemented in the excellent demo: Matt Pettineo - "A sampling of shadow techniques".
- Flip culling during shadow map rendering (trades acne for Peter panning).
- Normal offset shadow mapping does wonders for bias issues, but requires to have vertex normals around during shading.
- Variance based methods (ESM, VSM, EVSM) completely remove bias issues, but have other drawbacks (light leaking and/or performance issues).