Here’s the problem with the way the current system works. Let’s say you tweet something that turns out to be incorrect to your 100 followers. Let’s say 5 of those retweet it to their 100 followers. At this point, some 595 potential people have seen it. (Or at least spambots, but bear with me.) You realize your error, and issue a correction on your Twitter feed. Your 100 original followers may see the update, but it leaves 495 who do not unless those same five people again retweet you. In short, while the automatic retweet button on Twitter lets people spread information far and wide beyond your followers, there’s no way to makes sure those same people see your attempts to correct it.
So here’s one way it could work using Twitter’s metadata. Twitter could add a function, similar to a retweet or favorite, that let you edit and correct a tweet after it had been posted. Those tweets then show up in a timeline as having been corrected–again, they could be flagged like favorites or retweets. Click on a tweet marked as edited, and it uses Twitter’s Cards function (the same system that lets tweets embed images, videos, and text) to show the original.