You can share photos within the Camera and Photos apps, share your location from within Maps, send updates from Game Center, and post status updates with Siri. For that last trick, you can say "Post to Facebook I love reading Macworld," "Write on my wall I love Mark Zuckerberg," "Post I'm in the mood for brunch to Facebook," or similar alternatives.
To share photos on Facebook from the Camera or Photos app, tap the Share button, and then tap Facebook. The Facebook share sheet that appears will superimpose an album name atop the photo, which is attached to the typing area. Tap the photo to choose a different Facebook album for it. In the bottom right corner, you can tap to choose which audience you'd like to share your photo with; the options available to you will reflect your Facebook privacy settings. You can also choose whether to include location information for the photos you share.
Sharing your current location in Maps works pretty much the same way. You tap a pin, then tap the blue arrow, and scroll down to tap the Share Location button. Then choose Facebook, and you're greeted with the now familiar Facebook sharing sheet.
Again, as with iOS 5's Twitter integration, you can also save your Facebook login credentials in iOS 6's Settings app. In theory, other third-party apps that need access to your Facebook credentials could then ask for permission to use your Facebook account, without your needing to login again.