This is possible solution for being able to play Mafia Wars2.
Well this works for me!
1. go on account settings in Facebook
and click on account settings option, as it is shown in the above image.
Pick Security Option! - shown in above image
On the top find Secure Browsing and set it disabled as is shown in above image.
For me, Mafia Wars2 starts loading, I am able to play today.
Wish you luck!