Please check if all your plugins are up-to-date. To do this, go to the Mozilla Plugin Check site.

Once you're there, the site will check if all your plugins have the latest versions. If you see plugins in the list that have a yellow Update button or a red Update now button, please update these immediately.

To do so, please click each red or yellow button. Then you should see a site that allows you to download the latest version. Double-click the downloaded file to start the installation and follow the steps mentioned in the installation procedure.

Start Firefox in Safe Mode to check if one of the extensions (Firefox/Tools > Add-ons > Extensions) or if hardware acceleration is causing the problem (switch to the DEFAULT theme: Firefox/Tools > Add-ons > Appearance).

• Do NOT click the Reset button on the Safe mode start window or otherwise make changes.

• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

Make sure that you allow the plugin-container process in the firewall.

• http://kb.mozillazine.org/Plugin-container_and_out-of-process_plugins

You can check for problems with current Flash plugin versions and try these:

• disable protected mode in Flash 11.3 and later
• disable hardware acceleration in the Flash plugin

• http://kb.mozillazine.org/Flash#Troubleshooting

Problem solved! I downloaded and installed Firefox 24.0 Beta. Apparently Mozilla programming team made all the right changes in the new release. Now all videos starting working on Yahoo and BBC.

Link: http://www.mozilla.org/en-US/firefox/channel/#beta