Twitter's artificial character constraint is a boon. Some thoughts on how this improves your writing:
Lexicon/voice. To minimize character usage, I often have to shift to the active voice, remove nominalizations, or consult a thesaurus to obtain pithier words that equally or better describe a thought.
Forced precision. Good writers are exact and accurate in their use of language. Twitter is superb practice: it forces you to set down your key ideas with clarity, always.
Less regrets. It's easy to ramble. But it's hard to write concisely -- you have to think.
Laconic phrases. If the community of comedians, scientists, mathematicians, and philosophers can express deep, witty, sharp and lucid thoughts in 140-characters, so can you.