How to fix boolean cut failures? I refer to the Blender built-in boolean tool described here.

I am cutting a complex surface > 30 000 facets.  All the cuts are along coplanar surfaces.  About 50 % of the cuts fail.

In the detail of the cut file posted, you can see that the boolean cut seems to be done, but that the tris are not removed.

What can I do to ensure that the boolean cuts do not fail, or is there an easy way to remove the tris after the cut failed?

See this large sample cut file. 

Overall shape


Detail


Thanks.
To repair this kind of damage I would select all and press X (Delete) to start from scratch. 

Very similar result you can get easier without booleans and with clean topology by shrinkwraped edges over your terrain.


Add plane, slice it by Ctrl+R with value of desired amounth of cuts
Select one short edge, search for Select Similar > Lenght and delete them (X)
Subdivide all long edges in amount of desired detail
Rotate in desired angle of Z axis
Add Shrink Wrap modifier with Projection type, Target your terrain, Z axis, Positive, Apply
Select all vertices, Extrude (E) in Z axis, move below terrain level, Scale in Z to 0
Add Solidify modifier to get thickness


Simplified sketch of proces


Hires model (1000 slices)