Since Winamp 5.0 (and including 5.02) if Winamp (in classic skin mode) is minimised on closing, when you next load it the Playlist Editor and Video windows will be shown. This is not intended and both of these windows should be minimised.
The plugin below fixes this problem for Winamp 5.0 to 5.02 (it is built in to not work on versions after 5.02 when it will be added into the Winamp program code).
if the playlist window does not appear correctly (with the list shifted to one side) then you just need to resize the window and all will be fine. This will be correctly handled when added to the Winamp code