The "idea" of the veranda bothered me at first, but the reality of it did not. As many other threads have addressed, the doors are.....difficult at best to open, even for an adult. Between the lock being above my head and the weight of the door, it's not easy. The railing is high, and yes, while there are chairs/table, if you keep the door closed and locked and only take your kids out there while you are there, it would be extremely unlikely for anything to happen. Yes - if you leave the veranda and leave your child alone, then of course there's a danger - just like letting your child cross the street alone or as another poster said, like taking a bath alone.
I always have a weird dream before a cruise about this - and I always feel 100% better as soon as I'm in the room and try again to open the door and have to tug and pull! Then I sleep easy the rest of the time!