Recently, the question has come up on a forum how to cut a mesh (with the Disconnect command), and subsequently how to select certain colocated points. Cutting a mesh creates duplicates of points along the cut which are on top of each other so the normal selection can't "grab" a specific one.
Same issue with certain parametric objects that you polygonize: caps of cylinders (unless you create a single mesh) share point positions with points of the body, so it's not always clear what you selected until you move the selection.
Image shows the different disconnects: by polygon, by edge, and by point. The selected point was colocated with its "twin" after an edge cut and needs to be moved by itself.
The script PS_SelectPointByProximity helps with that issue.
You need to assign a keyboard shortcut to it, and also assign the same shortcut with shift and control qualifiers (as the C4D shortcut system happily collides with the qualifier concept). I put it on Y, shift-Y and ctrl-Y although you may want to use a different key, as Y is already used for "redo".
Now, if you are in point mode and have a polygon object (or several) selected, position the mouse over a polygon and press your shortcut.
The script will select the point of this polygon that is closest to the hit point. If that point is colocated with other points, these will not be selected. Thus, you can specify a single instance of colocated points easily.
Have shift pressed to add that point to a selection. Have ctrl pressed to remove that point from the selection.
Note that just pressing the shortcut will clear the previous selection, but only for this object. If you have selected multiple objects in the object tree, their selection will remain unaffected.
If you have issues running the plugin, or ideas on how to improve it, feel free to leave a note.