There are three possible causes for this issue which are intersecting triangles, small marked Constrained Lines, or there are very tiny holes in the polygonal surface causing the patch lines to "bunch" up around them (boundary edges).
1) To correct intersecting triangles you will need to perform the Repair Intersections function along with other polygon clean up functions in the Mesh Doctor.
2) If there are small holes in the polygon surface. You will need to take the model back to the polygon phase and fill those holes. Try the following steps:
To find the holes go to the Display tab and turn on Holes.
The green lines represent holes in the model.
Using the Fill Single tool, click the edge of these tiny boundary edges one by one till they are all gone.
Or unselect the boundary edges of the model and click Fill All.
3) The third reason for the "spider web effect" may be due to boundaries in the polygon model, which became constraint lines in Exact Surfaces Phase. Unconstrain the lines and vertices by removing the boundaries in the Polygon Phase.