browser fail?
Ok, FF has extensions and blocking is an obvious one, but why not have an option (on by default) which stops running flash/animated gifs/video if the tab isn't the active one? If you wanted to be clever, you could run the animations for 30 seconds and then freeze them if inactive. Perhaps put a little "pause/play" button on the tab to continue playing media in the background.
Judging by my wife's browsing habits, it isn't uncommon to have 20 tabs open (often on the same website) all with their little flash adverts and applications running. At that point, CPU resource becomes more of an issue than battery!
As a side note, I put noscript & flashblock on everything and my wife hates it. Too many of her shopping sites just break and she finds it frustrating. It's interesting to see a non-techy reaction to what to me seems like a very easy to use system.
As has been mentioned, it may be the moving graphics, not inherently flash which causes the problems.