As to challenging a pastor publicly? Well I don't know. Most instances of disagreement really should be taken to task privately, and the subject matter should be of utmost concern. Questions one should ask: Is it of importance to salvation? Is it something that is truly dangerous to the sheep? There is no doubt in my mind that the Lord may prompt someone to challenge a speaker publicly though I also believe that is probably the "exception and not the rule".
Jesus definitely confronted the religious leaders of His day publicly, while He had no earthly authority. I suppose He could have been considered a coward for not going to them privately, but He knew their thoughts and intentions. The Holy Spirit today still knows peoples' thoughts and intentions, and He can reveal that to us. Having said that, it would also behoove each of us to examine ourselves and our own motives before thinking we know someone's thoughts and intentions. IOW, before we would be so bold to stand up to someone publicly, we had better know what we're talking about lest, as someone else said, "we disgrace ourselves and our Lord".
As to writing letters, I have personally never received a letter (as of yet) regarding my policies or teachings (since I said that, I will probably get one now). However, a colleague of mine receives them regularly even though for the most part we are very similar. The biggest difference between us is if someone comes to either of us, I tend to be more willing to listen, whereas my colleague tends to be very unapproachable and wordy, leaving people feeling frustrated, like they're not being heard and their concerns don't matter. It's conjecture, but I tend to believe she gets letters because people don't believe they can really say to her what they need to say without being cut off.