Tweetbot - When replying to a tweet, swipe down to see the original tweet and author.
/via Kevin S.
Twitter - If you follow a “Tweet” link when not signed in, the Twitter dialog window allows you to sign in & Tweet in one action.
/via Rich Dooley
Twitter - When submitting the same tweet twice, an error message is shown.
/via Sindre Sorhus
Twitter for mac - After typing the first few letters of a word, pressing the ESC key will show a list of words that starts with those letters.
Edit: This is a native feature of OSX and works in some other apps as well.
Twitter for Mac - After installing the app, right click on any text in Mac OS X to see a tweet option.
/via Brendan Lee
Offcial Twitter app for iPhone - Dragging down the whitespace of reply screen shows what tweet you are about to send reply.