I've done a couple of serialized pieces for Twitter (Burnpoint and #OIA), and have come to some preliminary conclusions about the process.
#1. Spontaneity be damned... a serial needs to be written out ahead of time, rewritten for emotional punch, and edited for a smooth story arc and maximal value. In other words, it needs to be treated like just about any other long-form piece. I have another serial that I'm working on, but I did the Burnpoint serial to see if it could fly off-the-cuff. I had the plot mapped out and gave myself an hour or so in between each tweet to think out the phrasing.
#2. You cannot make it an fundamentally episodic work with an overarching tie-in plot, like Nicholas Nickleby. The 140 character limit makes it impossible to have clear episodic action AND maintain a plot thread that will run through them all. Tweets have to be unrelated nanostories, or they have to function like bricks in a wall.
#3. Gimmicky though they are, I like using word forms and agrammatical structure to convey meaning. Like e.e. cummings poems, the way the words are arranged on the page matters as much as where the specific line breaks are. A term like meta-textual content is appropriate here, but that's WAY too academic a phrase to toss into a blog. Regardless, Twitter really doesn't lend itself to that. A sentence broken off in the middle, with no concluding punctuation, can convey shock. A string of disconnected words can convey rapid action. However, these are really only useful when applied very sparingly, and they have to have a body of standard text against which they can be juxtaposed. Twitter just doesn't have room for that sort of thing. A string of tweets using conventional English grammar and sentence structure will look fine as they stand alone, but tweet #13, with a meta-textual twist, will also have to stand alone. From what I've done here, I don't think it can. Or rather, I don't think that I can do it in an effective way.
As always, I invite better writers to please step up to the plate and show me how it's done. Hell, I'll even buy you a cup of coffee as we talk about how you did it better than I did.