Gestures used judiciously
I agree with John Gruber at Daring Fireball: gestures are a handy option for certain people, but not the primary way to navigate any app. There's a nice benefit when many apps use the same gestures (like the now nearly universal "pull down to see new stuff" motion), but when it doesn't work, or it gets confusing, it's a bad experience.
Carbon uses gestures as a kind of shortcut for those who need them. If you're fiendishly updating your stream every few minutes, you can pull down from the very top to refresh, and use two fingers to skim to the top of your timeline. The whole timeline tilts, too, to register and recognize your insatiable demand for more, more text from people.
Pulling from the left edge of the screen brings up the switcher for multiple accounts. That's not something everyone will use, obviously, but those who do need to monitor and tweet from multiple names will find that always-on access convenient.
The conversation view in Carbon is just great. The tilting and transparency of the initial tweet, after you've pulled up the responses, is clever, but the reverse-chronological view of the following tweets is smart.
The option of using the "Last Taken" photo when adding an image to a tweet seems like a really smart time-saver.
It's much more apparent which account you're tweeting from while writing, and how to switch to a different account, than with Twitter's own app.
This might be a simple thing left out of the app in its early release, but I like it: the notification settings are dead simple. Carbon checks every 15 minutes, rather than the instant or 5-minute defaults of Twitter. You can turn mentions or message notifications on that 15-minute recurrence on or off, and that's it.
Filters, and lots of them. Specifically, you can keep multiple filters running for usernames, hashtags, or keywords. TweetDeck offers filters, but only one running at a time on Android. Carbon filters as many things as you want out of your timeline. For those of us with friends who can get obsessive about sports, Apple announcements, the weather, and more, it's a handy feature when it's needed.
Little animations, data points, visual cues, and highlights that grow on you, even over the space of a few minutes.