Are there child safety locks on balcony doors in balcony staterooms?
We were just on Explorer of the Seas about two weeks ago, and there was some sort of lock on the balcony door, but from what I recall, it was somewhere that the kids may be able to reach it depending on the age/height of your kids. Do keep in mind as well that the balcony doors are a lot heavier then the sliding glass doors at home and the handle has to be in the exact right spot to open it as easily as possible.
Depending on the age of your kids, I recommend setting rules about being on the balcony with them. Our kids know when they are in their own room with a balcony, they have to ask permission before going out there and that they are never to stand on any of the furniture on the balcony. We remind them of these rules several times during our cruise, and have luckily never had any issues.