They had an experimental project called 'annotations' where you could attach 1k of json to each tweet, like a DIY microformat.
I got onto the beta and created a prototype twitter client which you could attach mini 'apps' to tweets based on the payload type, e.g. you could tweet out a poll, or an inviation to play a game or a job advert or whatever, and you could attach your own app as a listener.
I think it could have been pretty amazing, basically A Message Bus For Everyone. If you build this yourself, you will run into the chicken and egg position, twitter could have pulled it off as they had the eyeballs and the developers.
Unfortunately they pulled the plug on it, around the time they started to close down the ecosystem.