Figured it was polite to let folks know how I'd "solved" this - since
it seemed to be redrawing the icons as the list item class changed, 
I made the icon part of the list item instead of being the style
list-style-image, and that has resolved the "jitter".   Still not sure
why it showed up on some machines and not on others, but it seemed
to be related to the speed of the machine and the screen resolution, so 
perhaps it was still redrawing, just faster than my eyes could see! 
Although I swear it was actually moving to a slightly different position
on the screen - oh well, as long as it's not visible now, I've got other
issues to worry about.  

Thanks for the suggestions, 
Susan