The thing people love about Twitter is its immediacy. You can post something about a subject that a lot of people are focused on and get a response almost immediately.
It's like fishing when you can see a massive school of fish circling around near the pier. Cast your line into that area repeatedly and you're bound to catch some good sized fish.
So, timing is important. You've got to know when your target market will be swarming on the site. Quite often a regular mainstream media event will attract them. TV shows are good for this. There'll be many tweeps watching it and tweeting madly at the same time.
Take the Aussie political show Q&A. Just about every Australian political junkie on Twitter watches that show, tweeting their thoughts with the hashtag #QandA. If you take advantage of this and offer some good observations you're sure to get some retweets and mentions and thereby raise your Twitter profile.
Of course not everyone's into politics. But there must be other shows related to different niches where the same conditions apply.