The transform widget is quite far away from my selected vertex in edit mode?
The transform manipulator is located at whatever you have set to be the pivot point which is not necessarily at the location of the current selection
See the manual http://www.blender.org/manual/getting_started/basics/transformations/transform_control/pivot_point/index.html
Sometimes a selection will select more than you wanted to select, and the widget, if set on median point (the default, I believe) will suddenly be somewhere you don’t expect it. Switch your view to wire frame, and look for selected vertices on the back side of your object, and zoom out to see if there might be some selected vertices off screen.