I haven't used Slackware recently, but this most likely a Firefox plug-in problem. There are several versions of the Flash plug-in available, depending on which distro & desktop you use, and it is possible to have more than one installed at the same time. In openSuse 11.1 with KDE 3.5.10, I had a problem on my laptop playing video on the BBC News site after updating to FF 3.5.3, and it turned out to be that the updated had added the latest SWF plug-in without removing the old one. I did that manually, and it is now fine.
I'm currently running FF 3.5.2 on openSuse 11.1 KDE 3 on a 32bit laptop and a 64 bit desktop with no problems, and after some tweaking I also have it up to speed on Windows XP Pro 32 & 64 bit. Interestingly the rendering performance on the 64bit 3.4Ghz XEON is not much faster than on the 1.6Ghz Celeron M. The main speed improvement is on opening and closing applications, and being able to have multiple files open in GIMP with almost no lag when swapping between them. There seems to be a slight speed improvement between FF 3.5 on Suse over the same set-up on Win XP, but that might be prejudice.