The Twitter application has had a major update for iOS devices to incorporate push notifications for @replies, direct messages and @mentions.
Twitter v3.2 for iPhone, iPad and iPod touch also fixes a bunch of bugs, enhances the graphics for the smaller devices' Retina Screen and also adds inline media tab for iPad which harnesses all of your saved searches.
There's also one-tap support for geo-tagging your tweets and better displayed shortened URLs. The improved app is free to download or update from the App Store now.
Now every time you're mentioned, replied to or messaged you'll recieve a notification, which for major league Twitter users could become a little incessant.