Putting a fully automatic mini-Uzi into the hands of an 8 year old is the irresponsible thing. The show supported the idea of using the full sized Uzis, but they weren't firing fast enough for Daddy, he wanted to video his sons using a zipper gun.
The show staff shouldn't have granted his request, should have said 'this is the best we'll do, you're welcome to get your own license'. And Dad's place was helping his son, not taping it.
Criminal charges? No, sorry, as sad as events turned out, there was no criminal actions by anyone, even idiot Dad.