Twitter released an update to its iPhone app last night that offers push notifications for mentions/direct messages along with other enhancements. The push notifications offers an alert instantly in real-time for the app. The full change log of the update Twitter for iPhone app are as follows:
iPhone:
* Push notifications for @mentions and messages
* Improved display of shortened URLs
* Correctly load reserved Twitter.com paths, such as http://twitter.com/newtwitter
* Fix connection error caused by a device clock being set incorrectly
* Additional retina graphics
* Enable geotagging in your account with one tap
* fix itunes links
iPad:
* Inline media
* Manage saved searches
* UI improvement
Download the latest verison of Twitter 4 iOS here