Besides all the normal things that can go wrong with a dam, I am concerned that even a minor shake or tremor could open up an earthen dam and make a real mess of things. Does Tim Matson or anyone have some suggestions on how to increase the structural integrity of a dam to resist earthquakes for those of us on hillsides in California or other earthquake prone areas?

Good question! As in, I've never been asked that one before, probably because of the scarcity of earthquakes in Vermont. But my first reaction is to suggest that
if there's anything to prevent the cracking like an egg of a quaked pond, it might be something relatively new in the pond building world: membrane liners. I can
imagine that an earthquake would not have to be world shattering to fracture a carefully made dam, or the basin itself, in a strictly earthen pond. At the very least
a tremor might induce some hard to track down leakage... not to mention a larger quake creating a leak that turned into pond destroying erosion... but
a thick mil pvc or other flexible material liner might be able to rock and roll a bit and even if the basin lost a bit of its integrity... still hold water. Opting to go with
a liner is a big choice design and expense wise, so if not needed for water holding reasons, well, if quakes really got you quaking, I'd look into it.
Tim