There's Always a New Tweet
I don't spend much time tweaking my UI, but I do attempt to minimize distractions. New mail notifications, badges showing unread messages, growls of all shapes and sizes, all these have a very poor signal to noise ratio, and rarely do they impact my current priority.
Do you have a Twitter icon like this in your menu bar?
Using the default settings, the birdy turns blue when there's a new tweet in your timeline. The problem is, there's always a new tweet. Asking your Twitter client for timeline notifications is like letting Mail.app check for new messages every 5 minutes, or welcoming people to stick their head inside your door at all hours.
Diverting your attention means losing your momentum. An hour with 1 ten minute interruption is more productive than an hour with 10 one minute interruptions, so if you have to lose focus, make sure it's happening for the right reasons.