Cursor weirdness

[Philip Herlihy]

I'm trying to connect tonight to a machine I've accessed many hundreds of
times.  Nothing has changed that I'm aware of, except that the pointer
doesn't seem to be in the right place.  I can't click on things, and I've
just noticed that when I move the mouse I get the familiar dot and also a
flickering pointer some distance away on the screen.  There is an offset of
(say) 300 pixels.  What could be doing this, and how can I fix it?
 
Phil, London