Are you working in NURBS or Polys. Vertices are found in polygons only and Isoparms are found in NURBS only?

Are you switching back and forth? Not recommended.

The points in NURBS are called CV's and the Isoparms in polys are called Edges.

If you have added isoparms or edges to any geometry then there should not a problem with then moving the CV's or Verts. maybe you have items turned off when you are in component mode?

Can you post a screenshot?