I hear you. The fragments drive me nuts. My exception is people who update with a statement like a succinct blog post, such as silly_imp has done here rather than posting their half of an ongoing conversation, the missing bits of which aren't included in the Twitter update so I have no idea what they're actually talking about. A collection of tweets like the ones in that example run very close to the brief "X Random Things Make A Post" lists that people use once in a while.

Twitter strikes me as very time-consuming. Not the actual posting, but the keeping up with everyone throwing sentences at one another all the time.