Maybe Twitter could use the hashtag system to accomplish this?
2. Make replies work better. Relax the character limit for replies to several hundred characters, make replies threaded, make low-quality replies go away, and high-quality replies float to the top (just like HN). Remove the line noise by having @ and # symbols not show up in the feed. Hashtags and mentions also shouldn't use up any characters. If all this happens, it will become reasonable to have actual conversations on Twitter.
3. Stop showing me duplicate tweets. Once I've seen a tweet, I shouldn't see it again if it's reposted (something many media outlets tend to do frequently).
Actions like this will make Twitter a better experience for regular users, and should help to kickstart growth.
4. Charge whales (those with the most followers, who disproportionately benefit from using Twitter) actual monthly fees.