Twitter have now sorted out the affected tweets and issued an all-clear. Here is the notice on their status page:
We’ve identified and are patching a XSS attack; as always, please message @safety if you have info regarding such an exploit.We expect the patch to be fully rolled out shortly and will update again when it is.
Update (6:50 PDT, 13:50 UTC): The exploit is fully patched.
If you don't already use a desktop client, use twhirl to sign in to your account and remove any offending tweets the virus might have sent on your behalf.
To be honest, it does make you think: people/businesses have come to rely on Twitter as a communication channel if things go wrong, but what if Twitter itself goes wrong? There should always be a contingency in place, within reason.
Here are some tweets about the topic:
For your convenience, here is Twitter's status feed:
No channel data