Daniel, if you open Settings.app -> General -> Location Services, can you check and see if the "Allow the app to use location information" setting next to OmniFocus' icon is turned off?
If it is, that should cause the screen behave as expected. (Though we should probably have an error message there rather than a black screen - I'll write that up.)
If that setting is turned on, I'm not sure what would cause this; contact the
support ninjas and we can investigate with you. Thanks!