Are we talking very small children, toddlers? You thought it was hard to childproof a house before. Anything breakable anywhere would go into storage. Hanging lights would come out. Padded surfaces wherever possible to avoid a boo-boo. It would be easier to keep them in a padded room.
Older children? Keep them on a leash. You'll have water balloons dropped on everyone. Planespotting. Pets afraid to go outside, until they learn to trust their carriers, then they'll pant to go for flyies (with more unwelcome bombs). If they want to hide and sulk, you will not find them.
Under World. It rocks!Bullying, alienation from other children, frightened parents and teachers, a need to understand responsible use of their powers (Great power, great responsibility, yadda yadda.), problems with figuring out that other children aren't like them, etc.
The Chosen One. The One To End All Light. Or maybe just eat all your ice cream.

Okay I have a bizzare baby boom, eight thousand kid's with superpowers, they all can fly. Any issues flying might cause?
Life's Gonna Suck When You Grow Up... But Is It That Great Now?... Also I'm Skylark2 now.