Twitter is vulnerable to SMS spoofing. All you need to know is the mobile number associated with the target account, and then you can use an SMS gateway to spoof messages. Facebook and Venmo (a mobile payment provider) were also vulnerable, but they fixed the issues after I notified them (Twitter didn't).

Timeline:

17 Aug 2012 - I notified Twitter about the vulnerability via their web form.
20 Aug 2012 - Twitter Security routed my report to their mobile support team.
6 Sep 2012 - Twitter asked me not to publish until they have fixed the issue.
15 Oct 2012 - I requested an update on the issue, and receive no response.
28 Nov 2012 - I notified Twitter that I would publicly disclose this issue.

http://titanous.com/posts/twitter-facebook-venmo-sms-spoofing

Cheers,

Jonathan