Push notifications for any @replies and DM's and even better would be to have configurable notifications, so you can, say, get notified for any tweets from a particular group of users.

Allow a setting to choose how often iTwitter should refresh to check for updated like 1 min, 2min, 3 mins etc

Currently iTwitter does not display a badge on the icon to show that new notifications exist. Notification popups can get overwritten by notifications from other apps, and if that happens the badge is the only way of telling that we have new notifications waiting.

Make tweets and have you tagged (@replied) show up in a different color to stand out better.

How can i refresh the avatars of any users? They changed it a week ago but itwitter shows still the old avatar.
Is there a trick?

Twitterific has a great feature for helping you stay under 140 characters. The compress changes common words such as "and" to "&" and other common abbreviations for words

Push notifications should only occur when the application is closed. Currently, push notification pop-ups popup while iTwitter is open. This really is not what push was intended for since we can just "update" or refresh the page.

Nutshell: Push pop-up notifications should "disabled" while application is running.

Sometimes, particularly after just starting the app, the text entry screen for new tweets seems really really laggy and unresponsive and can take several seconds to pickup text entry

Allow urls to be shortened using bit.ly

It would be useful to have an advanced search function. For example: search only in screen names

Currently, I change to Tweetie to view nearby tweets just because it shows their location as a part of the tweet.

Them both together as one app would make it the best app at Itune Itwitter 3D???

Mainstream Twitter Apps for iPhone are desperately lacking in TweetPhoto intergration. It is relatively new compared to TwitPic but seems to me to be much better. Giving users an option to upload photos to TweetPhoto would be a huge plus.

Allow . prefix for RT. Currently, this reply workaround to Twitter's 'fix' for replies is broken by iTwitter. This may already be fixed by the coming RT mods.

currently no way to reply from user profile, so very difficult to reply to user, not current follower, in another follower's tweet, or to new followers for that matter.

Usually only happens with first few tweets

Users' images change - it would be nice if the list of followers (and co.) updates images