SU's Intersect is problematic. It almost works.
It does however skip lines, will not intersect a very short face, causes surface flatness issues and tosses in unwanted hidden lines. There seems nothing you can do to prevent any of that.
Keep in mind, Intersect does NOT split the object, as you want to do. It only draws a common dividing line where the 2 objects intersect.
That being said, there are a few things you can do to correct or ease the correction.
First, It is best to draw your helicopter in a half-hull, as a component, then copy and flip its side. Move the copy on axis to join the 2 halves. Make the "dividing" line hidden or at least soft so it won't show later. That will eliminate the intersection operation. Any gaps along the dividing line are easy to spot and fix.
But, say you need to split something along a plane or a shape. (no pun intended) First make that dividing plane/surface a group, so it does not interfere with the objects geometry. Move it into position.
Edit the object and INTERSECT WITH MODEL. It is faster and better to pre-select only the faces that will actually be intersected by the plane. This prevents other intersecting objects to be intersected as well, adding to the cleanup job.
Now you can delete the intersecting face group, but best to wait until finishing fixing stuff.
There are a few things you can do to split the object, either delete the 1/2 you don't want and/or group/comp the part you do want. You can also group/comp the other 1/2.
Now comes the tedious part. Edit the cleaved portion. Hide the rest of model.
Closely examine along the perimeter of the split, looking for line fragments extending or face gaps along the line.
For extended lines, where it has no faces on either side, unhide the model and draw a line from the next vertex to where the line should end, then to the opposite vertex, using the plane group as a reference. 2 faces should form. Delete the line fragment.
Almost always, Intersect will miss only a single segment between 2 points on the split perimeter. Just join them endpoint to endpoint and the missing face should form.
If not, do a very small select lasso on each point to ensure there is not a tiny invisible line fragment, preventing the face. Delete those fragments, and redraw the line. This may also cause other adjacent faces to disappear, and you need to fix them too. Like I said, tedious work.
In many cases, that line may be very tiny, so it may be better to move one vertex (endpoint move) onto the other, eliminating the need for the line, but delete any fragments first.
Surface "unflattening" and extra hidden lines are related. When Intersect does its job, it sometimes cannot put an intersect line in place where an object line is very close to it. Upon cleanup, SU interprets the original objects line as an intersect line, and that causes a surface to unflatten, with hidden lines added to take care of the folding. We are talking less than .001 inch here.
If you need to zoom in very close and get near field clipping, then zoom out and turn off Perspective view. Now you can zoom in as close as you want.
The best way to fix this is to move the endpoints of the line onto the surface of the plane, forcing the face to reform and the hidden lines to hopefully go away. You need to use the MOVE+ALT to move the endpoints, and an axis (red, green or blue) direction. If the plane is not axis oriented, you may have to move the endpoint 3 times (each axis) to get it properly placed on FACE of the plane face.
There are also Pluggins that may help move endpoints onto a flat intersecting face.