Just from the breaking news viewpoint rather than chatter, the one twitter account I've seen really move stocks (for now) is @CitronResearch. I'm not saying I think their opinions are great, just that their tweets move the stocks.
Other than that, I have not found many instances where news breaks on Twitter. It can be helpful though, after a stock moves, to just search that stock symbol to see what the reason is if you aren't seeing it elsewhere. You just have to ignore all the people who are just saying "$HUM $WLP just went BOOM. LOL!"