We had our boy Will out on the boat at 11 days old. Wasn't much of an issue, but then we've got options on where to put him and plenty of shade. For the first summer (he was born in June) we didn't use the boat as frequently as we'd have like.
At the age of 8 months we took him for swim lessons (this past winter).
http://www.infantswim.com Mainly to make sure he'd be able to come back up to the surface at least once. He took to the classes well. I'm confident he'd have a clue what to do should he accidentally fall into the water. At least for long enough for us to fish him back out.
This summer we've had him out every time we've gone. It helps greatly to have the air conditioned cabin. He rides in the cockpit with us, usually with my wife holding him. He's "less than pleased" about wearing the life jacket but he'll learn. He's not yet interested in swimming from the boat, but does like the kiddie pool. We fire up the genset from around 1 until 3 for his afternoon nap. I got him a Kidco PeaPod tent that he sleeps in back in the mid-cabin berth. The tent keeps him in place and he seems to like it (crawls into it readily when he's sleepy). He also sleeps in it overnight.
We feed him using a Phil & Ted's seat that clips onto the table. Either at the cockpit or down in the cabin, the cockpit being preferred because it's easier to deal with messes. We bring along a MacLaren umbrella-type stroller. It's much easier to stow than others. We also use it as a place for him to sit for his morning bottle.
Hopefully it will be less work to mind him once he's 3 or 4 years old. Right now it makes up for the work I've put in running the boat by having my wife mind him all the time. I could not even considering taking him out without another adult aboard to mind him.
Oh, and he's learned how to slam the throttle into full reverse. I had to step up to the bow to deal with a stuck anchor and in a split-second between my stepping up and my wife taking the wheel, he got in there and yanked back on the stick. Pulled a fair bit of rode outta the windlass damned fast but otherwise caused no harm. The point being YOU NEED TO WATCH THEM 100% OF THE TIME.
Be especially concerned about how quickly they can climb up seating. There's a great risk of them getting up to the gunwales or other edges and being tossed out due to waves/wakes. They're FAST and you cannot let them climb unattended.
For the first 2-3 years I don't know that I'd try getting them out on an open bow boat. There's just not enough shade or a quiet place for them to nap. For short trips, sure, but not for an all-day excursion.