The Java plugin that you see in "Tools > Add-ons > Plugins" is used to run Java applets.
You only need the Java Console extension (Tools > Add-ons > Extensions) if you want to check and debug Java applets.
You can uninstall and remove Java Console extensions, you do not need them to run Java applets.

See:

• http://kb.mozillazine.org/Java#Multiple_Java_Console_extensions

Thanks, I wasn't aware of the fact that we didn't need it to use the Java. Most appreciated for the info :)

You're welcome.

Do you still have the problem with the videos?

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

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

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

• Don't make any changes on the Safe mode start window.
• https://support.mozilla.com/kb/Safe+Mode

Sorry, but these solutions read like an alien language to the casual user. I just want Firefox to work, and the constant updates disable things I've taken for granted. I can no longer see videos on certain websites, and the solutions here tell me nothing. I'm more and more inclined to stop using Firefox and switch to Chrome or something. If it ain't broke, why do they keep breaking it?

You usually only get such errors if security software is preventing Firefox from updating files as required. If your security software has a virtualization or sand-box feature then that is a possible cause. ZoneAlarm Extreme Security and AVG are among those that have it.