My iPhone is iPhone 4 with iOS 6.1.2
After installing MOLOME app on my iphone, i cannot access/use Facebook integrated service on the app. Twitter integration is okay, but not Facebook.
I did some googling and found that many people also had this problem, but no solution as of yet.
I went on to try many different things and finally figured out what went wrong with FB integration.
You need to log out of Facebook integrated on your iPhone (Settings -> Facebook), so that MOLOME is calling Facebook service via Safari. Once the safari opens up, just login/allow the service to be integrated.
Voila! You can now use MOLOME to post on your Facebook Wall.