In this case the grid effect on the map was caused by the amount of geometry on the low poly object.
To remove the grid effect on a baked map (cycles/BI):
- On the low poly object, Modifiers >> Add Modifier >> Subsurf >> use the default >> apply
- Create image for the map: UV Image Editor >> Create new (choose wanted size and rename), select the new image in the Node Editor so it is active
- Select high poly, low poly, go to edit mode so uvs are visible
- BI: Render >> Bake >> Bake Type: (choose map type, ex. Displacement), [x] Normalized, [x] Selected to active, [x] clear, Distance: (choose distance, ex. 0.18), Bias: (ex. 0.125, usually about 50-70% of the distance number), Margin: optional (default is ok) (should also work in cycles with cycles defaults)
- Bake (without grid)! :D
If your object has less polys you may have to up the subsurf modifier to level 2 instead. My low poly had 1008 quads in this case and lv 1 worked to remove the grid. Also as a side note, in zbrush I started to have the grid appear again at higher poly counts (at the equivalent of a level 3 subsurf) for the low poly so it is kind of a test what poly count works best for the map problem. Usually about 4-5k poly is a good number to bake from to avoid the grid.
Example of fixed Blender displacement map: