I honestly couldn't get location data to work on the Facebook app after just downloading it on my Galaxy Nexus.
I did get it to work after going to the Facebook menu and changing the "News Feed" option. It didn't matter whether I selected Most Recent or Top Stories, but it changed the way the app looked.
Here is what the app looks like after you first load it (in landscape to preserve privacy of friends):
Here is a screenshot of the new status update screen after switching it to Top or Recent Stories:
In order to share your location just click on the position flag which is in between the tag a friend and include a picture icons. I hope that fixes your problem.
Image source: GPS For Today