Any widget moves inadvertently to the left whenever it is placed in the upper right area of the window?
This was a bug that was fixed in version 2.4, see http://help.arcgis.com/en/webapps/flexviewer/help/index.html#/What_s_new_in_2_4/01m300000011000000/
I don't have this problem on my flex map.
On further read my first solution didn't seem to relate. But it is obvious that there does seem to be an edge offset perhaps the active area for the widget is a different size screen resolution?
BTW it does the same thing in the lower right. and to a lesser extent on the left edge. It looks like there is a different extent defined for the widget that for the map.
I had the same problem.
I think is a bug in flexviewer. Look at line 299 & 300 in WidgetTemplate.as:
if (widget.x > (systemManager.stage.width - widget.width - 200) ) widget.x = systemManager.stage.width - widget.width - 200;
That "200" make the movement. If you remove this 2 lines or you put "0" instead "200", it will be fix.