Because of the growing transition, efficiency, etc. and the ubiquitous nature of the iPad, many YouTube videos are encoded in HTML5 and don't require Flash. You may have watch some of those prior to hitting a video that only has Flash playback, at which point your problem presented itself.
Since the gold master build and I think the build before that, probably 70% of YouTube videos for me have just sat on the swirly "loading" animation. Downloading/updating a new build of Flash hasn't come to mind because I haven't noticed Flash not loading elsewhere. This also wasn't a huge issue to trouble over just because I can copy a YouTube address and it copies into a program called JDownloader to download the video really fast anyway.
But yes, yeah, I just mean to say that you're not the only one. I haven't tried any downloading-of-Flash solutions yet so I can't speak for it either way.