Random (and not loud) clicks is a strange one.
How frequent are they?
Do you still have the a860? If so, you might hook it up to verify that the clicks weren't there before (you may have been listening more closely after the new AVR). You know how obvious the sound is and how closely you listened to the A860 before, so this may not make sense. I'm just trying to think of something to help troubleshoot.
What is upstream from the AVR? Are you playing CD's? Have you verified it is not linked to the source?
Maybe @TLSGuy or
@M Code might have some ideas. I am not sure they would bother to look at a thread with this title, but pretty sure they would check it if it was titled "Random clicks from AVR", so I notified them.