Birdfeed [$4.99 - iTunes link] bills itself as "A very nice Twitter client for your iPhone". That's pretty much spot on. It doesn't try to razzle-dazzle, or focus exclusively on one element or another, but what it does do is provide a quick, clean, interface to manage your Twitter account (or accounts).
Highlighted features include the simple design, local caching of already-loaded tweets so you can keep reading when/if offline, SMS-style handling of direct messages (DMs) to help keep the conversation flow, unread @mentions (replies) and DM counters, and time stamps to indicate where you last read up to should new tweets have since been loaded.
To answer the immediate question, no support for iPhone 3.0 push notification yet. Birdfeed's Twitter account says that feature is likely, but there's no time-frame yet.
TwitPic and yfrong are available for image posting and tr.im for URL shortening. (Where's the bit.ly love, and tinyurl for retro chic?) Instapaper is supported, though you have to exit the app and go to the iPhone's Settings app to find and set it up. This makes sense given Apple's preference for keeping Settings in Settings, and also because it's unlikely you'll have to do it more than once.
Great from a user experience perspective, when you get to the end of currently loaded tweets, Birdfeed automatically starts loading older ones. That's right, no button tap required. (The default is 20 but you can change that in Settings). To get newer tweets, however, there is the perfunctory big honking -- yet tastefully rendered -- button at the top of the tweet list.
For users who put capital letters in their Twitter account names, there's currently a bug those accounts to go missing from the app, but it's known and a fix is on the way.
All in all, Birdfeed is exactly as presented -- a clear, consistent, and enjoyable general purpose Twitter client with some great new ideas in a even greater UI.
More screenshots after the break!