I have this very same issue. When I start my machine and log into Unity, one of the first things I will launch is Firefox. The icon in the Unity bar flashes a few times and then nothing.
I go to into System Monitor and find 2 Firefox processes there...one that is a zombie and other sleeping. If I do a 'strace -p ' on the sleeping process, it shows it is stuck on FUTEX_WAIT_PRIVATE.
This didn't occur when I was on 12.04, just since updating to 12.10. I've also seen the suggestion to disable the Firefox add-ons for Unity Desktop, Unity Websites, Global Menu Bar Integation, and Ubuntu Firefox Mods. I've done this, but get the same result.
Now, if while in System Monitor I kill the sleeping process, I can try to relaunch. Typically the 2nd launch works fine. But the first never does.
I'm thinking this still has has something to do with Unity, even with Unity integration add-ons disabled, because if I use Gnome or XFCE for desktop management...then Firefox launches fine the first time, or any time.