I accidentally posted to Twitter what was supposed to be a direct message. Now, people are replying to me and asking me about that tweet.
Can I delete it?
You can delete your old tweets, just click on the "trash can" icon. However they may remain around for a while in searches and the like. They'll also stay on people's Twitter home page until they refresh the page.
Voila! Gone forever... almost. Deleted updates sometimes hang out in Twitter search. They will clear with time.
When you mouse over the tweet it will darken and "Delete" will appear in the lower right hand corner, just click that. A confirm box will appear warning you that the delete cannot be undone.
if you wait too long to delete the status, chances are good it's going to stay on google cache and/or twitter-indexing sites for a while. once it's out there, it's pretty hard to get rid of permanently.