Thanks for getting right back to me. On the animation being somewhat exaggerated, that's true. Especially since it turns out there are two different behaviors from Opera, and it's way exaggerated compared to the "normal" behavior.
So actually I just noticed something very specific about the problem case.
If the server sends the file length back to Opera, then it slowly fills up the taskbar icon, and that's not a problem at all.
The real problem is when the server doesn't send the length, so that Opera doesn't know how big the file is. Then the animation is rapid and repeated. If I could go back & edit the original comment (don't think it's possible) then I would indicate that this is the only problem.
For example, try and download this link: http://downloads.dell.com/FOLDER01916806M/1/SUU_740_Q42013_A00.ISO.
Note that as soon as Opera prompts for a download location, the taskbar button starts animating rapidly. And then even after you've selected the download location, the button keeps animating rapidly.
Thanks again!