For those of you saying you have no sympathy for the mother...
Do you even have children? If so, if they've never run off... Well done. 
They've never run off in the park? Supermarket? Street? Road? Amongst the clothes rails in a clothes shop? Wriggled out of their buggy? Not even at least one of these?
Have your children always done exactly as you tell them, the first time that you tell them?
Do you have more than one child? Or at least have the experience of looking after more than one child? There are times when children excitedly run off. It's good that they do actually, they're asserting their independence. Sometimes it's safe sometimes it's not. If I were to go to a zoo, I would expect that appropriate safety barriers were in place, so that no human, especially and excited 4 year old human wanting to get a better look, could get past.
The mother had several other children with her. All it would've taken was for one of the others to distract the mother/ask a question and 5 seconds later the boy is out of sight.
The zoo is absolutely at fault. The safety barriers should be human proof. The child should not have been able to get past the barriers. A gorilla was shot dead, which is awful, but given the choice with what the gorilla was doing to that poor child, the zoo did the right thing and shot dead the animal.
It should not have happened, but it did. They made the right decision when they needed to. If that was my child I'd have no hesitation in shooting the animal myself, and I'd be very surprised if any other parent said differently.
If any animal hurt my children, I would do all I could to protect my child, endangered animal or not.