Lots of Intersecting faces when using 3d printing, how to fix them in batch? I am using Blender 2.7.8. 

I have a lot of intersecting faces on a peice I am trying to 3D print. My usual strategy in Edit mode is to manually delete each face, select the verticies forming it, and reform the face using F. This is unreasonable at this point. I have tried to select them all, and do a boolean operation, but that doesn't work (Intersect deletes everything, Union gives no improvement with all the faces selected).

What else can I try? Is there anyway to identify the real problem interfaces? Pic below. (Sorry for the Blue tinge, idk why screenshots on my second monitor always do that, #linuxproblems)
I hacked around this by:


Selecting all intersectng faces
Deleting only faces
Using Make Manifold


This reduced the number from 45 to 3, and I repeated the same strategy above on those 3 until there were 0.