Ignore the update Flash messages, there are no more for PPC Macs.
The last really supported Flash for PPC was 10.1.102.64, but if it's for like Facebook or such, people have been fooling FB to think they have a leter version installed.
Texas Mac Man's Flash hack/post...
It would help us to know more about the computer you are using and also the URL of the video causing the problem. There was a post very similar to this earlier today and in response to that one I noted I never have problems with YouTube videos and I run the last version of Flash for PPCs on a pretty old G4. I have not updated to the "hacked" version. Although the video could be the issue, I would have to see an issue myself (and I use Firefox) before I ruled out it being some other issue with your computer. You say your computer is crashing, not that you are getting an error message (until you disabled Flash completely). This suggests to me it isn't just out of date software. The hacked version isn't any more up to date than what I run, it just tells the server that you are running a newer Flash version than you are really using. If the video really requires a newer version then the hacked version won't help unless what is causing FF to crash is the error message itself.
Shockwave and Flash are different plug-ins (and shockwave is not required to play flv videos), maybe you should download the latest flash player for PPC:
Also, check this thread over adobe:
The hacked version to allow youtube videos to play on pages like facebook (I'm guessing you must install the Flash Player first anyway):
Adobe's Flash Player:
(use one of the UB DMG files to install)
(just replace the Flash Player.plugin inside /Library/Internet Plug-ins/, it's the main Library folder, not the User one)
Tried both links now, you should be able to download them