Quirks in web sites and web browsers are tricky....

* If the children-changed event is our current object, dump cache and
  also the context because all bets are off regarding whether or not
  our current location is stale.
* If the children-changed event is an ancestor of our current object,
  dump cache but preserve the context because something around us
  has changed, but our present location should still be valid. Plus
  subsequent sanity checks should trigger us to update things if
  our present location isn't valid after all.
* Otherwise, something elsewhere has changed so don't dump the cache.

Also add more debugging to get to the bottom of remaining quirks.