I got an answer on the OpenOffice forums:
- Select the polygon
- If not enabled, press F8 to enable the "edit point mode"
- Press Ctrl-TAB: you'll see one of the points selected (the first one considering the order on which the polygon was created).
- Press Ctrl-TAB again and again until you reach the point you want to move
- Now use the arrow keys: only the selected point will move
It works on AOO 4.0