A while back Twitter announced that their API would begin supporting the ability to specify what tweet someone was replying to. Of course this is a fantastic feature but there isn’t a single way users are benefiting from that information.
Here is my suggestion, put a “Replies to this Tweet” link next to every tweet. Here’s an example of why that would be unbelievably useful, often times I look at past tweets and see that someone asked a question that I would love to know the answer to. Searching for replies to that user can be helpful but if they are a popular user it is often too difficult to find replies to that specific tweet that asked the question.
A link sending you to a list of tweets made in reply to the original would make searching for information on Twitter infinitely more useful.
Update: apperently Twitter does have this feature, but it appears to only work when the tweet specifies which tweet it is replying to (this happens if the repliers twitter client supports it). I really wish that Twitter would have this feature for all tweets though, even if it just guessed by showing that users most recent tweet as the replied to tweet.