Firefox won't update its addons. Why?

It depends on how you have installed FF.

The default installation mode offered by the Ubuntu's packagers community is rather not coherent to the requirements of mozilla's products (this should be discussed with them if it hasn't already done) and breaks some features functionality.
One of this is the installation/upgrade of plug-ins and extensions not managed by the packagers community.
There exist extensions you cannot install or no more upgrade in a FF standard Ubuntu installation.

The only way to circumvent this, at present, is to install FF (or TBird) in userland by downloading it as bz2 archive from the mozilla site, copying the archive content to a directory, say /home/username/FF, and starting it from there.

In this way you have no more problems with plug-ins, extensions upgrade etc..

Beware! This solution may wipe away the precedent FF settings etc. you actually have on your PC.
If you are in the need to save the setup, bookmarks, hystory etc. of your actual FF installation, you have to rename the actual
/home/username/.mozilla
directory e.g. from a virtual terminal

>mv /home/username/.mozilla /home/username/.mozilla.old

Then uninstall FF by the use of Synaptic and proceed to install FF as explained before.

After having started the new FF installation once (and closed it again IMMEDIATELY!), rename the new and the old directories as follows

>mv /home/username/.mozilla /home/username/.mozilla.new
>mv /home/username/.mozilla.old /home/username/.mozilla

At this point you should have a functioning FF with your old setup, bookmarks etc. but your old plugins and extensions wich you must install from scratch!

After this last step you are able to install/upgrade etc. extensions, plug-ins etc. with no problems.

Regards