I had to do some research, and the following facts came to light.
1) Alec Baldwin was practicing a cross draw, where he pulled the gun from a holster on his left side, sweeping the across his line of sight.
2) While practicing this, the gun went off
3) Assistant director Hall handed Baldwin the gun, announcing it as "cold gun"
"A cold gun would be totally unloaded, nothing in it," said Zanoff. "A hot gun would be one loaded with a blank and ready to do gunfire. The guns should not get loaded until the first [assistant director] directs the armorer to load the specific gun.
From this I would say that the armorer was at fault, for providing the assistant director with not just a "hot gun", but one with a live round. Secondly the weapon, a colt peacemaker, is not recommended to "dry fire" the weapon, meaning you can damage the gun by the firing pin / hammer striking metal on metal.
Right or wrong, I imagine the armor would have put "snap caps" into the weapons to allow the actors to practice with them. And would inspection of the weapon have revealed there was a live round instead of a snap cap?
From Amazon:
45 Long Colt Snap Caps Peacemaker .45 LC Winchester Cowboy (6X w/Rubber Inserts) Price: $19.99
Can you tell the difference?