It's becoming increasingly clear that Twitter needs to follow Google, Microsoft, and Apple in providing two-factor authentication sooner rather than later. Such a system isn't foolproof, but it requires an extra level of identification information to authenticate with a service.
In addition, Twitter can do more to provide features that can help diminish the adverse impact of tweets and retweets that present erroneous information, such as some of the tweets that were sent during and following the Boston Marathon bombings. Twitter spawned millions of tweets as the events unfolded, including tweets that identified innocent people as the bombers and that were retweeted, passing the misinformation along. It's part of how Twitter works, but Mat Horan of Wired has recommendations about how Twitter could deal with bad tweets:
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.
Horan also suggests that the original author should have the capability to notify everyone who retweeted his or her tweet that there is a correction, which could also be displayed at the top of their timelines.
Twitter sent a note with the following response regarding the compromised AP account:
You may have seen recent reports involving news organizations' Twitter accounts being compromised. Multiple reports suggest that these attacks started through attacks on corporate email accounts. In the case of the Associated Press, this was confirmed -- the hacking of their Twitter accounts was preceded by phishing attacks on employees' email accounts.