Actually typically IIRC a producers job it to help pull together all the bits that are needed to put a film together, not to micromanage the set or set safety that is left to the department heads and safety staff or specialist advisors. A producer for example organises and arranges for key people to be involved, secures the script rights, finance and distribution. A lot of producers may never actually be on the film set, or only on the set for brief periods (most of a producers job is done when they've got the rights, money, distribution, locations and director arranged).
A director is the person who is actually in charge of most of what goes on the set day to day, telling the actors (such as Baldwin) how they want the performance ("draw the gun quickly, but smoothly, and point it at the camera"), the camera and lighting crew how they want a shot to look etc.
Then you've got the other "heads" who all have their own areas of responsibility on the set, and a producer won't tell a camera man how to handle a camera, or an electrician to wire something up a specific way (and is likely to get told in very short order where to go if he tries), but a director will tell them how he wants something to look and they'll try and do it, following their safety procedures.
If you expect an actor to check the inert or blank rounds in a gun are blank/inert every time someone hands them it, or they pick it up you're going to have some real issues in most action films where they do a shot of someone picking up a prop gun and using it as a single take as they wouldn't be able to do it. Likewise simply saying "you should never point a gun at someone" is not going to work on many film sets when the gun is going to be pointing at people, if just momentarily..