libavcodec has been updated in Ubuntu 14.04.
An update to libav-tools, libavcodec-extra and libavcodec-extra-54 in Ubuntu 14.04 has fixed the problem. The
libavcodec may be vulnerable or is not supported, and should be updated to play video notification no longer appears after updating the system with the Software Updater.
In Ubuntu 14.04, I am using the Firefox 50 from the default Ubuntu repositories, which is the latest version of Firefox at the time this is written. I do not have any libavcodec package installed in this system, because I do not need to install it. If you don't have a libavcodec package installed, you can ignore the second part of this answer.
I get a
libavcodec may be vulnerable or is not supported, and should be updated to play video. notification when attempting to play videos posted to Facebook and videos from other websites like cnn.com and yahoo.com. I decided to ignore this notification and not upgrade my libavcodec because the same videos play perfectly without showing the libavcodec notification in Chromium web browser in the same video players. The only difference in the videos between Firefox and Chromium that I noticed is in Chromium I see additional options to change the video quality when clicking the Facebook video player's gear icon that I don't see in Firefox.
update libavcodec notification in Firefox 50 when libavcodec is not installed
The notification in the above screenshot is a little bit confusing because the video on that webpage plays OK even when libavcodec is not installed. The notification appears to be coming from Firefox because the same notification shows on Facebook and CNN. Do I need to drag in another PPA to get rid of the annoying libavcodec notification in Firefox even though the video plays OK in Firefox without it? The same video plays perfectly in Chromium without showing any libavcodec update notification.
After you upgrade Firefox to version 50 (without libavcodec54 installed) and start playing a video, you may be prompted to Allow and Remember Firefox to run the video's multimedia plugin in order for the video to start playing.
To install libav-tools (Multimedia player, encoder and transcoder) libavcodec56 (Libav codec library) and libavcodec-extra-56 (Libav codec library (additional codecs)) in Ubuntu 14.04 open the terminal and type:
sudo add-apt-repository ppa:heyarje/libav-11
sudo apt-get update
sudo apt-get install libav-tools libavcodec-extra-56
sudo apt-get upgrade