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

He must respect the rank, saying hey man is not doing that. Inform him of proper military form. Semper Fi

As an NCO my guys and I were on a first name basis only because we had an agreement they give me their all at work an absolute 110% and we could relax while within the Platoon. Let me tell you morale was always high and any time I had to take leave my guys called me and checked on me when my father died my guys each sent flowers instead of one order for the group. The comradery you'll experience is worth letting your guys relax that being said these guys need to learn when and where because in front of a higher ranking officer or commander or senior NCO's it will not bode well.

Absolutely correct them. If you don't and the other see their actions they will think they can do it.

I you are a officer then that SPC need's to say Sir it is the Customs and Courtesies of the day as long has long as you are in the Army. Too this day I still do it an I been out 15 years it is part of my DNA till the day I am called too regroup an that is a long time off HOPE.

You should take them too the woodline and have corrective training on how to properly address officers. Hahahaha. Seriously though this seems like to be more to this. Maybe you guys were hanging out one night and you have become good friends or the E4 is being a douche bag. I would have a discussion with the E4 and reiterate the importance on addressing higher ups and any officers.

Absolutely. As an officer you should 'light him/her up', if you don't, You are derelict in your duty. I don't care if you're best friends or lovers off base, it's not the person that is being saluted, its the rank.
There were a number of officers I thought had no business being in positions of authority, but you always respect the rank.
Just like POTUS, you may hate the man, but it's the office you respect.

If you can't correct your subordinates, you shouldn't be in a leadership position. Man up buttercup. I work with plenty of retired officers now, most of which are hold lower positions than I do. If they don't respect me as a man, I make sure they understand what leadership structure is.

No, LT, you should always allow today's E-4s to do whatever they want l, whenever they want to do it. After all, you don't want to be reported for disparaging a subordinate. Best to just shake it off and carry on as though you're best buddies.

Seriously? I just can't even.

Absolutely address it 100% of the time. If he does it to you, he does it to other officers. A little humiliation now prevents a lot of suffering later.

During my military service I had many good friends who were officers - all the way up to Colonels. If we were sitting in the privacy of my house or theirs, it was Bob, Jim, whatever... In public, it was always yes sir, no sir, good morning Captain/Major, or whatever the rank was. I also was married to an Army Nurse -- we were married during the period from Staff Sergeant and Lieutenant to retirement at First Sergeant and Lt. Colonel. In private settings, is was Patti and Dean... In military settings it was by rank... Whenever she introduced me to other officers or enlisted persons it was always " I would like you to meet my husband Sergeant First Class McBride" - same thing went for me introducing her, Bottom line: The Specialist should never call you anything but Captain Railey or sir. An appropriate response would be for you to quietly remind/educate him of the military courtesies expected from both of you. I would not just "correct" him or reprimand him. Give him a chance to do the correct thing.