(...) it's just a problem with Firefox not properly supporting a certain mime-type.

Edit /usr/share/mime/packages/freedesktop.org.xml as root and replace the following:

<mime-type type="application/vnd.adobe.flash.movie">

With:

<mime-type type="application/x-shockwave-flash">

And then run:

sudo update-mime-database /usr/share/mime