Twitter is useful for getting tipped off about stuff that's happening, but frequently that kicks off a discussion, and it's really difficult to have a meaningful discussion on twitter (even when the people involved are capable of it). The messages are too short, especially when they start getting consumed with multiple @ mentions, and it's impossible to follow the course of a discussion with the half-baked way they try to thread them.
I feel like "half-baked" is being generous. Anyone who's ever tried to follow an endless series of "View conversation", "View other replies", and "Show more" links trying to trace the start of the discussion and see all of the comments knows what I'm talking about. It's especially a treat when you have to click "Show more" a bunch of times, then have to click something else to try to see more of the discussion, then try to go back and your place is lost.
I've heard that twitter may ease the limit on message size (maybe drastically, e.g. 10k), but I'm not sure how that would work in general, let alone if it would help with this problem (it definitely wouldn't with the half-baked threading). Perhaps it'd make sense for twitter to implement a feature like StackOverflow's comments + chat. For those unfamiliar, StackOverflow allows "short" comments on questions and answers. At some point, enough comments will trigger it to prompt users to continue discussion using their chat feature. (That may still have message length limits, but is just generally more geared to extended real-time discussion.) So tweets would be analogous to comments and the new feature would be a discussion / chat format that allows longer messages and makes it easy to see the whole discussion. Notifications would probably work differently for messages posted in the discussion format.