I have used blender for some time and have never seen something like this, I tried: Changing normals; Flat/smooth shading; deleting the faces; making the faces planar, and I can't find the solution.
Without viewing a file it's hard to say with certainty, but it appears that the 3 edges in question are slightly raised. If you have already checked normals, double vertices etc. then a possible fix for this would be as follows (using a circle):
If you do not have the Mesh: loop tools add-on enabled, then enable it in user preferences>add-on tab under the community add-ons.
Select all (in edit mode) and press W then choose loop tools>flatten
I would try removing double vertices and recalculating the normals.