Intersection is incomplete. The bug occurs in both V7 and V6. (I don’t have earlier versions installed to test.)
This bug appears to be caused by some “core” code which determines intersections and is used by numerous commands.
Simple single span degree 3 surface, not singularities stacked control points, split edges and located near the origin. The untrimmed surface is the “Original” surface in the attached file and images below.
IntersectBugDC01.3dm (1.6 MB)
Absolute tolerance 0.001
Angle tolerance 0.1
Intersect
a plane at z=15.000 with the surface results in an incomplete intersection of two open curves.
Trimming the surface as in “Trim A” below results in the same.
Trimming smaller as in “Trim B” below results in the correct intersection with a single closed curve.
Moving the intersection plane to z=14.900 results in the same.
Moving the intersection plane from to z=15.001 results in the correct, single closed curve intersection for all surfaces.
I have verified that this bug occurs using the follow commands.

Intersect
 as described above 
Section
 in the Front and Right views 
Contour
 when a contour is at z=15.000 or z=14.900 
Project
 when the line in the attached file is projected in the Front or Right view 
Split
 fails with plane at z=15.000 or z=14.900 
Trim
 fails with plane at z=15.000 or z=14.900
I did limited testing with planes and lines slightly tilted and the failures were similar.
My guess is other commands which use intersection calculation have the same bug with this geometry.
Z=15.000
Z=14.900
Z15.001