Given that this was a rehearsal, not a test of blank firing or a close up shot requiring dummy rounds, the gun should have been EMPTY. This is the BARE MINIMUM competency an actor can be expected to perform when handed a prop weapon. A simple visual check of the cylinder gap with the frame should have shown there was SOMETHING in at least one of the cylinder chambers; be it empty brass cases, a live round, a blank, or a dummy round. For this dry run rehearsal actually dry firing the revolver doesn't seem to have been necessary so Alec was negligent in failing to inspect the tool and in cocking and dry firing it in the direction of the crew instead of just mimicking the action and saying "pew pew" since the crew was in the line of fire and without protective precautions in place. Many other crew are also negligent.
Of note, this type of revolver is hard to quickly empty, each round has to be unloaded individually, even pushed out with the ejector rod if they were fired and the the case is stuck in the chamber. So I can see how a live round might have been left in and an incompetent series of inspections failed to identify it. You can't pop out the cylinder like on modern revolvers (in general, there are some break open styles, but Alec probably had a traditional Colt single action type revolver as those are by far the most common type depicted in Westerns) . This means it requires MORE on the part of the actor, possibly even pointing it into a discharge barrel and firing on all six chambers to verify whatever was in there was inert before calling the set "cold".
Given all the other screw-ups on this set I wonder if he had a gun belt with ammunition in it, and if that was live ammo he inadvertently loaded instead of dummy rounds or whatever they use in those things. Tracing the origin of the live ammo is going to be interesting (probably a hold over from the off-set target practice but it would be nice to know for sure by comparing the bullet and case from the shooting with the ammo they were plinking with). The thought that a scab could have sabotaged the set (and inadvertently got someone killed in the process) is terrifying. The previous gun mishaps likely point to incompetence rather than malicious intent.