Hi Christopher, you can usually only show points on individual surfaces, not on faces that are joined up with other faces in a solid.

You can extract the face you want to edit by selecting it and running Edit > Separate on it to break it away. Then once you have it as a single surface you can then turn on control points for the individual surface. There is some info on that here:
http://moi3d.com/wiki/FAQ#Q:_Why_does_show_points_work_for_some_objects_but_not_others.3F

But what kind of editing are you trying to do on the face directly? One thing to note is that on a flat planar face, the surface that is underneath everything is usually a very simple plane surface just made up of 4 corner points, then there can be numerous "trim edges" that live on that plane to form its trimming boundary.

When you edit surface control points you will not be editing the trim curves, you will be editing the "underlying surface", the thing that the trim curves are living on...

Usually for editing an extruded solid you would have the extrusion come from a closed planar curve rather than a face and you would edit the curve and re-extrude it (or if you have not done other operations on it you can edit the curve and let history update apply the extrusion again).

You can't really directly edit trim curves by pushing and pulling the face's edge curves themselves around, you usually edit regular non-edge curves in that way. If you have edge trim curves and you want to get regular curves from those you can select the edges and do a Copy/Paste to duplicate them as curve objects.

- Michael