Other half has my old G5 iMac, and it's doing her very well. However, this week, some YouTube videos a not playing - instead displaying a PlugIn Not Found error estate and then saying that the video can not be found.

Not all videos are doing that - I think that more recent uploads are processed for HTML5 playback. Recently, I disabled Java on that machine, but thinking that may be the problem, I renenabled it, but with no change. I also tried reinstalling Flash, but with no luck there.

Other that "it's a PPC machine, what do you expect" type answers, which I know is a distinct possibility, is this something others have come across here and is there a solution?

I am posting here as, yes, this is potentially a Mac hardware/software problem, but on Googling it, I have seen similar reports for Chrome, and am not convinced that this is a Mac only problem.

Have you disabled JavaScript?
Try re-enabling it if you have.

JavaScript is running.

Just a thought, but are you on Virgin broadband by any chance? There've been a string of issues with VM streaming video over the last few weeks.

If using Safari v4 or v5, go to this address...
http://www.youtube.com/html5
...and join the HTML 5 Beta. Wherever possible, videos will then use HTML if it's available - bypassing Flash Player.

If you prefer to use Flash Player, have you checked it's as up-to-date as possible? Adobe have now stopped supporting PowerPC Macs, so the last version available is v10.1.102.64 - check here which version it currently has installed...
http://www.adobe.com/software/flash/about/
(see the "Version Information" panel)

I have the 10.1.102.64 installer file if you need it - Adobe have made it all but impossible to find on their website - the newer versions of Flash Player are Intel-only, so the highest your iMac will ever run is 10.1, unless Adobe have a change of heart (unlikely)! PM me if you need it.