Split out from T142042. This appears to occur in all versions of IE except Edge (even IE11 on Windows 10, where T142042 did not occur). It seems to be caused by the fact that Monobook and Vector style the personal tools differently; the badges are display: inline-block but all the other personal tools are display: inline;, and this causes IE11 and below to push them down by 1em. Negative margins don't seem to be able to fix this, the only way I found was position: relative; top: -1em; but of course that screws things up in compliant browsers by moving the badges up off-screen.
