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

Your an officer and your really asking this. WTF

Yes you correct it on the spot that what RHIP is all about respect the rank earned

RU shitting me... As much as I disliked certain officers I NEVER disrespected the emblem they wore on their collar. It didn't matter if they were a boot Ensign or CincPack Fleet and yes I actually met him and he sent me a letter thanking me for the pictures I sent him of his visit to my ship while on a WestPac cruise.

Correct him.

Just my opinion- Wouldn't it be better if you can find a more senior enlisted person to help the E4? I messed up similarly when and E3, and got chewed on by a major- put it down to him just being a jerk. A couple of days later a Tech Sgt (E6) took the opportunity to help me learn and I never forgot that lesson, even to the point that, later in my career I suggested to a young LT that when our younger troops messed up it might serve our overall mission better for him to "correct" me and give me the space to handle it. IT got the job done and strengthened the chain of command.

First try speaking to him one on one and remind him of the rank structure of the US Armed Forces. You don't even have to necessarily give him a written counseling statement. However, you need to do a Memorandum For Record that day detailing what you discussed with him and why. If after you speak with him his action persist, he should be put in for 1 week of corrective training in full battle rattle, and be made to present a class in the rank structure and respect thereof to his Company's entire junior enlisted members. This "soft" approach is positive in two ways. First he doesn't get a record of UCMJ, and secondly, having to do a presentation in front of the E4 mafia will wake up other soldiers who are borderline disrespectful. I hope this helps. Taking $ and imposing UCMJ should be reserved for those actually deserving of it.

Dumb question. Hell yes correct him.

The very fact that an Army captain is asking a question like this makes me sad and angry at what the Army I served in has become. YES! Yes you should absolutely correct that SPC! I know my Army career came to an end 20 years ago but has discipline and education on military tradition, regulation and protocol really degenerated this far this fast?!

Beyond saying that you should correct this situation yesterday I will say that the way you correct it at this point is going to be important. As far as I am concerned you are at much, if not more, fault than he is for not correcting it the first time. Now, because you have in the past let it happen, it has become the new standard even if it is just a standard between you and him. I would not make a show of it. Do it privately, acknowledge that part of the blame is on you for being complacent about it but explain that proper protocol and adherence to Army regulation must be maintained. You can be friendly with the correction since it is your fault it has gone on. However, if the soldier cannot take the correction for what it is then you may have to become more forceful with it.

??????????????? You even asked this?? SMH

Soldiers should never bring the "hood" with them. They volunteered to serve and volunteered to meet or exceed the standards. If they cannot, or will not, do that they have no business serving in any capacity of any organization. Hopefully, you corrected him, forcefully.