When sharing a post from the previous version of Facebook for Android, you may have forgotten to tap the itsy-bitsy people-sharing icon before you sent it off to the Interwebs. This icon controls the settings for who can see your post, be it Public, Friends, or other groups you're part of on Facebook. Fortunately, this icon hasn't gone anywhere, but in case you forget to use it, there's a fix -- and it doesn't involve logging in on the desktop Web site.
First, make sure you have the most recent version of Facebook for Android. Just because you've done all updates from the Google Play Store doesn't necessarily mean that you're using the latest version. Many mobile app updates are done with a staged rollout, which can be quite annoying if you're not in the first group. The easiest way to check your current version is to go into the Application Manager (Settings > Applications) and find Facebook in the list. When you tap it, the version number will be displayed in the top area of the screen.
If you don't have version 3.3 you will need to wait for the update to reach your Android device, or install it from a third party (at your own risk). Once you're on version 3.3, follow these quick steps to adjust privacy settings for shared posts:
After a post is finished updating to Facebook, just tap on the three dots in the top-right corner and select Edit Privacy. Next, select the audience you want to share the post with. Now the post will be available only to the people you selected.