I had the following packages installed via Smart (from applications\internet):
firefox-1.0.7-1.1
mozilla-1.7.12-1.5.1
mozilla-flash-7.0.61-1.2
mozilla-swfdec-0.3.5-1.2
Plus Opera installed by rpm
Well, the first thing I did was google like a maniac for untold hours, to no avail. Next, I removed the mozilla-flash package, which disabled Flash period. Next, I attempted to install Flash by hand, using the Macromedia installers. Again, we have the same incorrect functionality as with the package. Conclusion - the mozilla-flash package is okay.
So I went ahead and uninstalled every reference to Flash I could find, and did a few more hours of googling. Nothing. Finally, I decided that I would start removing and reinstalling packages to see which ones had an effect. First, was mozilla-swfdec. After removing that package, Flash could be installed, and worked perfectly in all 4 browsers. Conclusion - the mozilla-swfdec package is screwy.
According to my information, the swfdec package is supposed to be some sort of Shockwave content plugin, of which there is no Linux version. However, in retrospect, it wasn't very good. Instead of seeing the missing plugin placeholder, I would just see white space. Great package

If you're having trouble displaying Flash content, take a look at your package list. You may find you are in the same boat as me.