When I use the Group Select, or the Direct Select tool, often the "anchors" will don't appear to be highlighted when you click to select. If you then hover your mouse over the points, they once again appear to be selected.
I've also seen instances of the opposite--when the top left (control panel) states "no selection," yet anchor points appear to be selected. (The points are NOT selected, as any attempt to modify using a menu choice yields a message such as "make a selection first.")