After clicking the Play arrow, move your cursor to the bottom of the video display area, a toolbar will pop up at the bottom of the video display area with video controls. One of those is Full Screen; mouse-over the items for a tooltip that describes each symbol on that video toolbar. Press the escape (ESC) key to exit full screen video mode.

• See - https://support.google.com/youtube/bin/answer.py?hl=en&answer=72689

Other - You need to check your plugins and update as necessary.

1. Check your plugins - https://www.mozilla.org/en-US/plugincheck/
2. Shockwave Flash 11.4 r402
   • https://support.mozilla.org/en-US/kb/keep-flash-up-to-date-and-troubleshoot-problems
   • https://support.mozilla.org/en-US/kb/install-flash-plugin-view-videos-animations-games
3. Adobe Shockwave for Director Netscape plug-in, version 11.6.4.634 (not the same as Shockwave Flash, Adobe Flash)
   • http://kb.mozillazine.org/Shockwave
   • Download, save, close all browsers, run the installer that you just downloaded and saved - http://get.adobe.com/shockwave/

You can't have only the YouTube video player in a Firefox tab without going full screen AFAIK.
That would involve to hide all other content with a use style sheet pr extension (this may be doable, but will be a lot of work).

You can select a larger player (there is an icon for that as well) and resize the browser window if you do not want to see the extra elements on the page.

Thanks for the answers. Sadly it was, what I expected. The full screen is no good, as tabs etc. then aren't available. Then I can only hope that someone invent some sort of add-on...

Tap the ESC key to return your Firefox window to normal mode with the tabs (when in video full screen mode).

Alternately, you can download and save the video to your hard drive, then open a separate video player and play the video which will not interfere with your current browsing, if you are just listening to a concert. You can switch back and forth between Firefox and the video player by clicking the appropriate icon in your Windows task bar.

• Good video downloader (there are others) - https://addons.mozilla.org/en-US/firefox/addon/video-downloadhelper/
• Good separate video player (there are others) - http://www.videolan.org/