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

Yes, You should,
you can do this one of two ways,
you yourself can correct the E-4 on the Spot, that not very satisfying to me, I Believe The Junior Member will not remember, how or why you corrected him .
I believe the Better way for the Officer to approach this behavior is to find the E-4 Immediate Senior Enlisted Supervisor, ask him Why his Junior Personnel do not Know How to Give The Proper Greeting Of The Day, or How to Properly address senior Personal? ask him is this what he is teaching his junior personal, then recommend ie: Tell The Supervisor that you want him to oversea this JR Member on Giving Training to the other junior enlisted members , On how to Give the Proper Greeting of the Day, and how to address senior personal , when Speaking to a officer or senior enlisted . after speaking to your senior enlisted leadership, they should be able to straighten this matter out without you being involved anymore in this matter , the Senior Enlisted will straighten the junior member out .

I guess it kinda depends however, I still call SGMs, SFCs and officers by their rank or Sir to the point they get sick of it. And we’ve all been retired for close to twenty years. Lol I do expect however, them to call me Sergeant Smith.
I would talk to his NCO and let them know that the Specialist requires some additional customs and courtesies training.

Of course you should. Why would you even ask such a question?

Military personnel is always on duty and subject to the UCMJ. Contact the SPC's NCOIC and recommend additional training on military customs, courtesy, and the UCMJ.

I drove for both company and field grade officers as a young (18-19) pfc and specialist. You should absolutely correct the soldier.

Something I learned as a driver was that when we were in the vehicle talking, it was ok to be somewhat casual, however, I never would have not shown the proper respect.

If you are complicit in this E4 thinking they have a casual, friend sort of relationship. I would own up to your mistake but definitely don’t let the standard slip.

My son is now an Army captain and we frequently talk about the importance of keeping the high standards with enlisted personnel and being the example for all the men in his charge because they will look to him on the battlefield.

Yes. Military bearing is part of military discipline. You correcting the enlisted and your peers to maintain military standards is part of your job, especially as an officer. These Joes and Janes are representing US Armed Forces. Even, I as an enlisted would correct you if you are doing something against the norm of the uniformed services. Furthermore, I expect you to do so on me as well if I am stepping out of bound, especially if I have left my fly opened. :) Never be afraid to do the right thing, just be tactful when doin it.

I’ve been retired for nearly 30 years. I haven’t been able to convince soldiers I served with to NOT call me “Sir” even though I’ve subsequently been a guest in their homes.

Fix it now CPT!

I would have put my jump boot so far up his fourth point of contact, it would have taken a combat engineer to dig it out. NEVER, EVER, allow such insubordination.

He knows better.

Sorry to say this;
If you have to asks this question, you are not an officer or most important a leader!