Operating system and graphics card
NVidia GeForce GTX 1060
MSi Dominator GT62VR laptop
Broken: (example: 2.69.7 4b206af, see splash screen)
2.78a, 2.79, blender-2.79.0-git.a8f11f5-windows64
When performing a boolean operation, sometimes it drops faces, creates vertices where there should be none, and generally mangles the output mesh. I was able to reproduce one of the problems with a very simple test scene. In this test scene, there is a box cut out of a triangular box object. The cutout looks successful as far as vertices go, but the inside face is not filled so it creates non-manifold edges.
Exact steps for others to reproduce the error
Based on a (as simple as possible) attached .blend file with minimum amount of steps
The object "InfillNegative" has a Boolean Difference modifier for the hideen "ToeCutout" object. There are two missing faces where the "ToeCutout" object has been subtracted, leaving a non-manifold "InfillNegative" object.