Comment 1 for bug 236887

This seems to be a xubuntu issue, since the save dialog is not part of gnome-mplayer/gecko-mediaplayer.
You should change the default save directory, that / means that your default save directory is the root of your filesystem, where you don't have write rights (you should have the same problem in other applications).
In gnome-mplayer there is a last_dir gconf key which is used as the default load/save dir, but I must admit I don't know xubuntu and if this key is honoured.

For the time being I'm closing this as it doesn't seem to be a bug in gnome-mplayer/gecko-mediaplayer. Perhaps the best for you would be to ask for support in the xubuntu forum or answer's tracker.

Please let me know if you still think this is a bug for gnome-mplayer/gecko-mediaplayer.