There are so many facets and levels of responsibilities to this topic, that it’s hard to talk about just one without at least touching on them all.

Leaders responsibilities. Like @patrick_d_moore1 stated, leader responsibility starts with ensuring all under your charge (to include yourself) know and understand DoD and local regulation and policy. Once you have that, show that you follow it with your actions and enforce it with your subordinates.  As Patrick said, the worst thing you can do is regulate thought and create and oppressive environment, but as a leader you can never let your guard down because there will always be “that guy” in your element that doesn’t think farther than the “post” button.  Don’t be the leader that forces your subordinates to “friend” you either, however let them know you and or your 1SG/PSG do bounce around looking at what people post publicly. When something pops up, leaders need to correct it swiftly and publicly, singling out the perpetrator(s) and not falling into the “mass punishment” trap that destroys morale.  Punishment/corrective training should then fit the level of offense; be it a verbal “don’t do this again,” a written negative counseling, administrative action (Art 15, letter of concern, formal reprimand), or relief for cause. However (not to open a can of worms), there is more than just Leader responsibilities here.

Battle and Individual responsibility. Like everything else, Soldiers need to be taught that they shouldn’t put themselves or allow their battles to get into situations that could end up compromising them or their reputations, or worse – endanger their safety. If Soldiers see a battle out of control, or doing something that will get them into trouble, then battles needs to step in (I had a situation in GTMO that goes to this very point).  Whether it’s deciding against policy to hang out in off limits establishments, getting or allowing others to get “out of control” during a night out with the “guys/girls,” or (I don’t know…) allowing someone to take/sending “adult” photos, there is some level of personal responsibility that needs to take place. Don’t be the “person” (insert your chosen acronym here) that shares something given to you in trust and confidence, however like I tell all of my subordinates (and kids), never take, allow taken, send, or receive anything you don’t want your parents or chain of command to see.

These are of course my opinions and thoughts, but in the end professionalism needs to be the end state.  Professionals don’t violate SHARP, EEO, or do any of the despicable things we’ve seen in the news lately.