I'm running Linux mint 15 olivia, Xfce 32-bit version. I try to access youtube videos in the latest Firefox, but the videos displays incorrectly for some reason. I do have flash installed, but I see there is more than one flash plugin that can be installed when I go the software manager. I installed Google Chrome also and there youtube videos displays correctly, I can watch the videos as normal. Why is this? What can I do to fix firefox? I can see that I have shockwave player also installed.
The reason you are having difficulty is that Adobe stopped releasing Flash for Linux:
For Flash Player releases after 11.2, the Flash Player browser plug-in for Linux will only be available via the "Pepper" API as part of the Google Chrome browser distribution and will no longer be available as a direct download from Adobe. Adobe will continue to provide security updates to non-Pepper distributions of Flash Player 11.2 on Linux for five years from its release.
The reason it works with Chrome is that it is part of the browser distribution.
Things don't look so hot for on-going support as noted in the Mozilla Support forums and elsewhere. There are work-around hacks in that thread, but I wouldn't depend on them.
I would recommend going to http://www.youtube.com/html5 and setting Youtube videos to play with HTML5. I don't think all videos have this functionality yet (I'm not sure), but this is probably your most futureproof option.