When an E-4 calls me "hey" or "hey man" knowing that I am an officer, should I bother to correct him?

Damn right you need to correct him while on duty. Off duty out of uniform thats a different story but the SPC should still show respect. Off duty the SPC should say Hi Captain or whatever rank he knows you as or hello sir. The Big Thing For That Young NCO To Remember Is RESPECT!

If you both know for certain the rank of each other, Yes you should correct him. The only situation I can think of that it would ok is if you are in a potentially dangerous location and pointing out your rank may make you a target.

Yes, I would suggest that you correct the soldier's language behavior toward you, sir. Try to avoid, "bother" in your language use here, sir. As professional soldiers, we react to whatever is before us based on our military training, among many other things. To be sure, this Soldier is highly likely to share with peers that he got away with a, "Hey man." with a commissioned officer. I'm sure your post will cause many of us old-timers to wince. But you indeed did the right thing to reach out for coaching, guidance, and leadership on this one. True leaders know this is important on a number of levels. His language use with you degrades good order and discipline--vital to unit morale, cohesion, and battlefield victory. When in doubt about any behavior I needed to undertake during my long military and civilian public-service career, I asked myself whether behaving in a certain way showed whether I was faithfully executing my Oath of Office, or that was I slaking off, just to go along to get along. Here, of course, the former is the high road and the right road. Thanks for your courage to serve! All the absolute best to you, sir. HOO-RAH! Airborne, sir!

Not to be rude but you are saying you are an O- 3 and don't know if you should correct an E- 4 for calling you "Hey-man"? My opinion is that your behavior concerns me more than the E-4

It is about respecting rank and the uniform.

It would depend entirely on the context. If it was a SPC that I didn't know and my back was turned to him where he couldn't see my face or rank, then I'd be inclined to give him a pass and just turn around and let him see my face and rank and realize his mistake. That's and honest mistake. If it was a SPC who knows who I am, or knows my rank and says that, not only do they get corrected, but I will also let their NCO know so they can ensure that the correction sticks.....usually with a little physical motivation.

Let it go for that one time. Unless it becomes it comes an issue.

As long as you are commissioned, whether on duty or anywhere on the planet. You are your rank and they are theirs. If you aren't wearing your uniform and they don't know you, lighten up Francis. If you aren't wearing your uniform and they know you, communicate your displeasure and expectations.

Only if you're in uniform or if he knows you're an officer. Really, how would they know otherwise?

Everything in context and right perspective. A standard is set for a specific reason, not any or all reasons. A great physicist once shared with me that we must be appropriate for the occasion. If I am told to wear a suit in front of my boss at work, should I be expected to wear a suit in front of my boss at the beach? No. I wear swim trunks. If I am teaching a class as a professor to college students, and I am addressed as Doctor, should I expect the same courtesy from a kindergarten student?

Or, a husband comes home from work and scolds his wife because the cupboards are bare while in the same instant 5000 Syrian children are gassed to death. In that moment, the husband's demands seem incidental. Context and perspective.