Facebook Places is not available everywhere. As of now, “Places is only available for US users.” However, when I accessed the app on iPhone yesterday, I managed to see friends’ check-ins list (see below), but no check-in button.
This morning, Facebook released an upgrade (version 3.2 to 3.2.1) for its iPhone app:
In the latest version 3.2.1, I can no longer see friends’ check-ins (as shown above). Instead, I see this: