A few expansion areas come to mind off hand:
1. Media distribution
2. E-commerce (get the hottest, limited supply thing)
3. Events & ticketing
4. Financial market alerts
5. AMA-style Q & As
6. Chat/AI services and integrations
This actually makes me wonder: if you increase or remove the length limits, how well would Twitter work as a private chat platform?
Because compared to the terrible internal "social platform" sites that some large companies run on their intranets, a company-wide private version of Twitter actually seems like a significant improvement. Use lists (including shared lists) as an equivalent to rooms or groups. That would give three different types of streams: your main feed (people you follow from across the company), the groups you watch or participate in (where most of the productive value comes from), and the firehose (to sample what's going on across the whole company).
As a bonus, if you add in a form of federated accounts, this could allow businesses paying for such a service to have a family of verified accounts on the public Twitter, all tied to their domain (similar to email addresses).
Facebook has a "Facebook at Work" enterprise product and, from what I hear, the company dogfoods its own platform for work as an alternative to email and mailing lists.
The idea may not be too far-fetched as Facebook actually does have an enterprise product, Facebook At Work. I think Twitter is too focused on other things to try it though.
6b. "Customer support in a box" services for companies that use Twitter to find and help customers with problems.
7. Micropayments: Twitter could monetize Likes using a Flattr-like micropayment system. Just add a "tip" button next to the heart button, to pay the tweet author $0.01. It could create a virtuous cycle of more tweets, more tweeters, and more idle funds in tip accounts for Twitter to reinvest elsewhere.