I believe this is a reference to the fact that the security guard who initially realized that the break-in at the Watergate was occurring found a piece of tape that had been placed over the door latch so the door could open even if locked. At that point, the guard called for additional help, the burglars were apprehended, and the process of following their trail, leading to the oval office, began. If not for the discovery of that taped door latch, presumably the invasion of the Democratic Party offices would not have been discovered.