Always have your cell phone on YOU, not in the cart. If you get pitched out, you need to be able to call for help.
I always wear a helmet, driving or riding.
Practice a routine to get the horse to the carriage, and do it the SAME, every time. I do one side completely, then the other, which some feel is not the safe way, but I usually hitch by myself, and do not want to forget something by switching sides back and forth.