If you have 2 observers facing one another, the observer that was on the ground first will update, sending a pulse, then the observer just placed will observe that observer's change, and back and forth. See video.
Should an observer be able to observer that another observer had a block update?
As of 16w44a, observers no longer detect block updates, but instead detect blockstate changes. And because observers have a "powered" state, one observer activating counts as a change in blockstate, and so the clock works. This behavior is, therefore, works as intended.