I normally have two WLMs running at the same time. I tile the windows so I can see them both at the same time. For one of the windows, if I shut it down and restart it, the window position is restored properly. For the other it remembers the position to be around 5 pixels higher than it was where I normally position it. No matter if I move the window where I want it to be, it moves a few pixels upwards every time I restart it.

Is this a bug? Is there a registry key than I can delete to reset the window position?

This forum is to report bugs which are found in Messenger Plus!, not Windows Live Messenger. Moreover, what you report is not a bug, that is how Windows Live Messenger works. Windows Live Messenger doesn't support polygamy by itself, so running two instances of it may not function correctly, rather it functions as how it is designed. I mean what you experience is not an incorrect functioning. When you close the Messenger contact list window, it saves the postion in registry and recall that position when you re-open it. Because only one position value exists for many contact list windows, the next windows will open in the first one's position and on top of it.