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

The biggest room of all is the room for improvement. Explain to him that in the military we have standard operating procedures and being respectful of one’s rank is military discipline.

You might want to bother to correct that SPC.

Unacceptable when either of the two is in uniform. If both are out of uniform (in civillian attire) still unacceptable. Sounds like Fraternization to have more than a brief conversation and casual meeting. Very few circumstances where Officers and Enlisted can interact socially on a familiar basis. All interactions should be respectful. Specialist (E-4) and an Officer (O-1, O-2,....) both need to go back to Boot Camp or Officer Candidate School, all of this was covered.

I would remind him of the appropriate protocol in a gentle way giving him the benefit of the doubt or accounting for his youth. The second time would be treated differently. Reminding him may save his skin if he assumes you letting it go gives him a pass to do it to others.

Should you correct him yes, however that doesn’t mean he needs to be lit up or degraded for this. A calm reminder of military customs will suffice. Then the SPC will remember you as that guy and not the asshole that nobody wants to come and talk to. I would also hope that when you have an NCO with you that he would immediately correct the issue before you had to.

Correct him, otherwise he will feel it’s ok in other situations in front of other officers away from work, perhaps your commanding officer.

You should absolutely correct him, its all about respect.

Yes!

The E-4 had poor NCO Leadership or.......he's completly ignorant.

Sir, ask yourself this question who is more wrong the soldier who made the error or the leader that saw the error, recognized it as an error yet failed to correct it?

I hope that answers your question sir.

Absolutely! On duty or off, you are serving for twenty-three hours and fifty-eight minutes a day, the other two minutes are yours's. Did you not notice that the twenty-four hour clock commences at 00:01 Hrs., and ends at 23:59 Hrs. Why? This is the Military way, on either side of the pond, to say thank you go and rest for a couple of minutes!
Let this slide and next thing you know, its caught on and discipline is hard to regain. In that event, I have known 1LT's to request a transfer. They may get it, but some Commanders, myself included will not transfer you, this to make you step up to the plate, demonstrate the authority of your Commission, demonstrate your skills, and respect to and for the enlisted, but ensure your command position is recognized, and never compromised. This can only occur by remembering that respect is a two-way street. Yes, you will need to be corrective in a plethora of different situations, never-the-less, YOU have to lead from the front.
Counselling is important, my modus operandi of Counselling was to ensure that the soldier was marched in by a member of his/her sex, as is the case in disciplinary situations, otherwise, compromise is almost a given. Following the formalities, I would invite him/her to sit, and give them the benefit of my advise, expectations, and how the future is anticipated to go. After the individual had marched out my Junior Officer was drilled a new one! "What were you thinking, wasn't this Officer 001 at OCS!?" By the by, MI5 already took 007!
Naturally, this does not apply to disciplinary matters, in this case the soldier remains at attention. Never, but never tear into a soldier in front of his/her peers, that remains the prerogative of the DS. Never-the-less, command is restorable. I would tell my junior Officers; "Times may change, but standards must remain.", A mantra that guided me in many situations, both soldiering and in clinical practice.
Good luck 1LT Railey, I wish you well, now, get on parade, "Hum a little tune and remember; you volunteered." Go, and be the officer you chose to be.