These days, social media channels are incredibly fast: within a few SECONDS your tweet might go around the Earth and penetrate throughout the Internet reaching users of all ages, races, genders, occupations and so on and so forth. As a public servant you have to assume liability for what you let out into the World Wide Web. However, a blogger from Canberra Craig Thomler suggests that in some cases it is appropriate for a politician or an agency to delete their post. For example, if they publish "a social media comment that is factually incorrect it is OK to delete the comment, provided they do so within a short period of time (within a few hours) and reissue the correct information". The reasoning behind this is that if wrong information starts floating around the web, it might cause harm to those who believe it and take it to action. If the information was offensive to the readers though, Mr. Thomler does not recommend deleting it but rather publish an apology through the same channel of social media but keep the original message. You can read the entire blog here.
Taking into account strict conditions of an event when a post or comment can be deleted, I think the point remains - deleting twits should be the last thing a public official should want to do, rather he or she should think twice before posting untested data.