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

If you are an officer in the US Army, you are lucky that SPC did not call you something much worse. Because I would. US Army officers are the most dishonorable, cowardly people on the face of the planet. After what my family had to go through at the hands of those pretenders and the fact that they refuse all accountability and refuse to fix their mistake, wifllful or otherwise explains everything smuck. Any other branch, officers should be treated with the respect that they earned. So you are lucky you got a "hey man." I love how you post this. Shows you are just as clueless as the rest of the US Army officer corps. Take a long hike off a short pier if you are Army. It will save unlimited headached among the enlisted that should know better than to look up to such officers. "An Era of Dishonor: the true story of Fort Benning Officer Candidate School class 01-06."

“Cheap cigar” is part the description of my response.

I am reading this as you were not "on post " when the SPC said "hey man". You were in the civilian world and OFF duty correct? My answer will be dictated by your answer.

Not all who join the military, officers or enlisted are bright and or astute. Let it go, not worth the issue. if this repeats on duty, call him or her to task

So, in my day, an officer would call in the subordinates NCO and let him correct the problem. If it was a 1 time thing, a good verbal lashing would work. If it was habitual, it went to wall to wall counseling and the problem was fixed. Its the NCOs job. Your job is to fix the NCO for not doing his job.

If the offices is out of uniform, and not on Duty. No I wouldn't address hem/her , the same way I would if she/ he, was in uniform and on Duty.
He/ she, should show me the same respect.

Best advice I can give you is to call 1-800-Waa! Ask them for a set of balls.

Yes, it is your duty to correct. If he does not learn from you, who will he learn from. When I came in the Army as a 21 year old college graduate, I thought I would never have to correct someone who had been in the Army for 3, 5, 10, 15 years already. Of course, that was not true. The Army structure is such that, fresh newly trained people (officers, junior NCOs) are required to remind and uphold the most basic of standards so that those who have been serving 15 or 20 years never become complacent and we remain a great fighting force.

Yes Rank should be respected by both NCOs and Officers

Do either of you have Ranger Tabs?