traveling with full black/grey tanks

Any tricks, precautions, etc about having to travel with a full or partially full grey and black water tanks? Some of the places we're considering boondocking at do have dump stations so we might be on the road for a while before we reach one. I seem to recall reading a thread about some bad experiences with this, but can't seem to find the thread now. We have a new 3124 with the Thetford Elctra Magic recirculating toilet (has the self contained black water holding tank).

Thanks