Dude I had the very idea =) Except mine was one word at a time. It came from an exercise we did in improv101.
I think you can make the UI a lot tighter. Imagine just a WHITE screen with THE story...constantly refreshing. Along with an inputbox at the top to add your contribute to it. Perhaps integrate with twitter.
The UI does need some work but I probably won't invest too much effort until I work out if the idea is viable.
One story is a bit hard for lots of people to concurrently work on unfortunately. Part of my strategy is to have short stories so that I can email it to the contributors when it is completed (hopefully within a day or two). Then I'm hoping they will forward the funny story to their friends (with a link of course).
I think you can make the UI a lot tighter. Imagine just a WHITE screen with THE story...constantly refreshing. Along with an inputbox at the top to add your contribute to it. Perhaps integrate with twitter.