It seems there is a conflict between WPMU Dev Dashboard and FontAwesome when viewing admin pages in Firefox.
I think WPMU Dashboard may be enqueuing an older version of FA, so when another plugin is used (such as Better FontAwesome) to add a nice icon selector to the TinyMCE, half the icons are missing in Firefox.
This issue is only in the admin side, and only in FF (Chrome is fine). I've narrowed it to WPMU Dev by doing a clean WP 3.9.2 install, and adding only WPMU Dashboard and Better FontAwesome plugins.
Once I disabled WPMU, all the icons are visible. When enabled, half of them are broken.
I have attached screenshots showing the 2 situations - you can see some (ambulance, anchor etc.) are broken when WPMU Dev is enabled.