In theory, an extremely useful magical item, since an omniscope can see everything. However, historically they were so difficult to steer and control that most were simply used as mirrors, because most of everything is nothing, meaning that most omniscopes showed only blackness, and wizards were generally looking at their reflections whilst staring at the dark heart of the infinite cosmos.
Recently, omniscopes have been used more frequently by the wizards of Unseen University, thanks to a couple of discoveries by the Professor of Inadvisably Applied Magic, Ponder Stibbons. Stibbons discovered (in The Last Hero) that when an omniscope is broken, every piece can see what every other piece sees. In practice, this means that two people who each have a part of the same omniscope can communicate.
Stibbons also discovered that the thinking machine built by his department, Hex, was able to steer an omniscope with relative ease and accuracy. This ability was exploited in The Last Hero to locate The Silver Horde, and in Going Postal to speak to Devious H. "Dragonbreath" Collabone in Genua.