A problem arises when an author of a record only intends for a certain audience to retrieve that record in the future. Search engines (such as Google) are designed to grab as much as possible about a subject so that the user can quickly make judgements about that subject, sometimes without even clicking on a link. For example, if someone has been charged with a crime but not convicted (not found guilty), shouldn't Google's results display that the person isn't guilty? Often it wont, potential employers might see that the person has had legal problems and immediately dismiss them as a potential employee.
Another problem with maintaining privacy (while using the internet) is that information is often sent through a maze of different companies that, unlike ARPANET, can harvest that information for their own interests without the public's knowledge or permission. Encryption has helped keep email, passwords, and financial information more secure. However, there is always someone out there with the means to defeat the encryption. Whether that's a government, business, or individual, the internet is certainly (unfortunately) not a place to communicate private matters with the expectation of totally secure transmissions.