Facebook SDK 3.1 for iOS - runs on iOS6, but crashes on iOS 5.x
Did you set the frameworks to be optional? When you are adding AdSupport.framework, Social.framework, and Accounts.framework, there is drop down menu to the right that you can select between "Required" and "Optional". See a picture example here:Link
Another thing to check is in your Project's "Build Settings" that 'Base SDK' is 6.0 and 'iOS Deployment Target' is iOS 4.3.
I'm able to build FB SDK 3.1 on my iOS 5.1 with these settings.
For anyone reading this and using Facebook SDK 3.6+ for iOS, you no longer need to include these libraries or Optionally link them. See the Facebook docs for Upgrading from 3.5 to 3.6:
"Remove the framework dependencies added to your app when you installed the Facebook SDK. The SDK still depends on them but now loads them automatically making setup simpler. Remove these frameworks / libraries:
libsqlite3.dylib [or remove the -lsqlite3.0 linker flag]
[Note: if your app uses any of the APIs from those frameworks / libraries directly, your project should still include the framework explicitly]"