If you've made sure that you have the Facebook icon active (highlighted) on the New Tweet screen but tweets aren't appearing on Facebook, you may need to reset the connection.
Please do the following:
Go to www.facebook.com and go into Settings and tap "Apps".
Make sure visibility of app is set to Public. If not, set this setting to Public and try again.
If it already is set to public, but your posts aren't appearing, tap "Remove app"
Go into TweetCaster's settings --> System. Verify that use Facebook is enabled. Then tap Facebook login reset.
Return to the New Tweet screen and tap the Facebook icon and you will be asked to log in fresh.