Hi Duke, what you are calling "control curves" there are probably edge curves of surfaces.
Those are part of the definition of a surface, you can't normally just grab them and move them, the actual surface data is something different than those edges. This is what is called an "underlying" surface which is a lot different type of a system than a polygon mesh system where each polygon "surface" is exactly bounded by an edge.
That kind of "edge is the natural boundary" can happen with NURBS models, but once you do any kind of trimming or booleans, you get internal trim curves instead of "natural boundary" trim curves.
There is some better description and illustration of this in this FAQ:
http://moi3d.com/wiki/FAQ#Q:_Why_does_show_points_work_for_some_objects_but_not_others.3F
That gives some examples of how an "underlying surface" works and how trim curves work where they are internal to the surface.
This system in general means that you can't just turn on control points for any booleaned solid and yank the points around like you would do in a polygon modeling system. So from that standpoint it is a negative thing.
However, at the same time this system is also one big reason why boolean operations work so much better with a NURBS system than with a polygon modeling system. When you do a boolean or trim, the actual underlying surface remains exactly the same and instead new trim curves are created on the surface. This prevents the surface from dicing up into ten zillion little tiny slivers like happens with polygon booleans.
Anyway, is there a specific reason why you want to remove those edges that you were showing? It is not necessarily an "error" to have them.... Although it can be good to reduce them in areas that you want to have completely smooth since when you have one larger surface it is easier for that to be smooth rather than something made up of diced up smaller bits. But to do that you have to create surfaces in larger sheets initially, like sweep them with longer curves, etc... instead of trying to remove them afterwards.
Hope this might explain things a bit more, I am actually currently off on vacation for a week so I may not be able to give you a whole lot more specific help directly on your model until next week.
- Michael
