We raised our son on the boat and besides some other issues, most of what has been said above is very valid.
Our rule was, and is, all children wear a life jacket at all times. Little ones wear one with a crotch strap.
Swimming lessons are also very important, Daniel started them when he was about 18 mos old and took them for many years. He enjoyed the lessons and to this day is like a little fish in the water.
During docking, Daniel usually kept me company on the flybridge. There were few rules except that during docking everyone stays in one spot and is quiet. To this day, Dan will sometimes remind guests that they need to be quiet when Dad is docking. He also became responsible early for the engine shut down. Once my wife had a line or two on the boat, I would go down and help secure the boat. When complete, I'd call up for him to shut the engines and electronics off. This made him feel a part of the procedure and instilled responsibility. His duties now include setting all the circuit breakers in the correct positions, starting the engines, piloting while underway (with direction from a sighted guide). He sometimes gets anchor duty (with a windlass) but this still makes his mother very nervous.
Dave, the biggest danger your 3 yo faces is the current in your area. He needs to be taught to swim towards the shore if he falls in, not to try and make it back to the boat. If he is really active and/or a bit clumsy, you can also have the netting installed around your railing system to minimize slips and falls into the water.
Just remember that no matter what you do, as soon as you make the boat dummy proof, they'll invent a better dummy.