If a producer has a questions or suggestions about any production values of a show, the producer should bring those up to the director privately. If a playwright has suggestions or input on a show, it should also be done privately with the director. The director wields absolute authority over the actors and crew (at least, in theory, the director should). To keep a show on track, such authority should never be questioned publicly.
While I have directed plays several times, I rarely direct my own plays. I actually prefer to direct works by others, and as a playwright, I prefer that the premier productions of my works are directed by someone else. The main reason is to test my playwriting. That is, to see if what I put on paper stands alone. If possible, I attend rehearsals to watch the progress, red pen in hand to update my script. Occasionally an actor may ask me about the meaning of a certain line or clarity of some point of the script. But usually, I'm a silent observer of the process.
Sometimes in an initial production of a script of mine, the director may request that a section be worked over or re-written, and so I do that. But eventually, as things progress, there will be a point in time that changes to the script must cease so the actors have a baseline against which to memorize. I, however, don't stop with the notes in my script. Those are the changes that I think will help the script, but that we don't have the time or talent to implement in this particular production. After the show is over, when I go back to do the extensive rewrite, I'll incorporate all the changes noted, both those that made it into the production and those that didn't.
