Hi Mike,

> (there seems to be a point where an object doesn't let you
> see the points anymore)

You'll always be able to see them if you use Edit > Separate to break things into individual surfaces.

It's when you have 2 surfaces that are joined along a trim curve boundary that you won't be able to see the control points - that's to avoid you pulling some points of one surface and opening up a gap in what used to be a joined common edge.

See this FAQ entry for some more explanation:
http://moi3d.com/faq#Q:_Why_does_show_points_work_for_some_objects_but_not_others.3F

- Michael