More news on my video card front.
As per
http://kerravonsen.dreamwidth.org/914772.html (wherein I discover that there are problems with Firefox on my NVIDIA video card display, and blame the Nouveau driver)
and
http://kerravonsen.dreamwidth.org/915062.html (wherein I discover that the NVIDIA binary driver is even worse)
My initial diagnosis is confirmed, because Arch Linux just updated the Nouveau driver, I installed this newer driver, and my display problems have gone! No more odd behaviour with certain images on certain web-pages, they're all displaying okay. Yay!
It's a great relief to know that my monitor isn't dying, as suggested by
droxy. Whew.