Twitter now allows you to search all public tweets, all the way back to your first tweet. Now's the time to delete anything you regret.
Entrepreneur explains how you can use Twitter's archive function to download your tweets. The archive function isn't new, but the ability for other people to search old Tweets is, which makes this download feature much handier.
The archive file is CSV formatted, so you can open it in any spreadsheet program. Once in there, you can search for keywords you might want to expunge. Then click on the link and delete the tweet in question. If you can't remember what you'd like to delete, focus on a time in your life when you might have said something you regret. Some good starting points are times when you had trouble in your job or relationships.