Try uninstalling the Flash you have currently installed (it looks like you might have a beta version?). Restart your computer, then download and install http://fpdownload.macromedia.com/pub/flashplayer/current/licensing/win/install_flash_player_11_plugin_32bit.exe.

If that does not work, Try to start Firefox in Safe mode. This mode disables all extensions, user customizations, hardware acceleration, etc. temporarily for diagnostic and troubleshooting. If Firefox works fine in Safe Mode, then this is likely an add-on issue. Restart Firefox in normal mode, then type "About:addons" (without the quotes) in the address bar. Disable your extensions one by one, restarting Firefox between each one, until you find the trouble maker. Once you do, you can disable that add-on and report the issue to that add-on's developer.

Thank you for your answer. The problem was with the Flash plugin; the version you submitted works as it should. It's quite odd that Adobe releases plugins that are faulty to begin with.

Continuing with this problem, now with Firefox 14.0 (Build 20120605113340) and Flash Player 11.3.300257, the videos appear again as blank. I noticed the following article: http://kb.mozillazine.org/Plugin-container_and_out-of-process_plugins . The problem is that I cannot find dom.ipc.plugins.enabled.<filename> mentioned in this article for Flash, only dom.ipc.plugins.enabled, and when I set this to false (originally true), the videos work. Why is that?

Why 32 bit and not 64? Why is not Chrome plagued with these problems - it works straight away.

Google Chrome includes the Flash plugin, whereas Mozilla is all open source. Firefox doesn't include software which isn't released under an open source license.