Bug#826227: Acknowledgement (gnome-session: Mouse Acts Strange After Awhile)
Further investigation has lead me to believe that this is a hardware issue. Think replacing the mouse is in order. So, AFAIC this bug report may be closed. Excuse the noise.
Bug#826227: Acknowledgement (gnome-session: Mouse Acts Strange After Awhile)
Forgot to mention that I'm using left handed mouse, so in Gnome Control Centre that option has been set for left handed use.