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

This isn't even a question. I'm a guy who's not overly strict on formalities but this is ridiculous. Officers are ALWAYS to be called sir no matter what. By correcting them you are actually doing them a favor. If they continue to do this eventually they will do it to a psycho who won't be so kind about it or to someone who is offended but won't say anything and rather go tell they're NCO, platoon SGT etc. and that will cause a big scene. Lay down the law.

The Spc. should be corrected. In my 30 yrs, officers were always "Sir and Ma'am". unless they invited a less formal address, off-duty. I always told my subordinates that this was the key.
MSG Mack Ca Mil res (Ret)

So are you still an officer off duty, or do you leave it at the door when you get off shift. Is the SPC still a SPC when he is off duty or is he just a dude. Ugh, YES Gunny speaking here YOU are an officer Sir. Period. This could be handled with "The Look" you can do it. Channel that basic school Chief you had you can do it.

I read through some of the responses to this question, and they range in severity from the far left to the far right. Based on the fact that there's so many opinions on it, and only one actual answer (and you know damned well why) makes me fear for my country's safety. If we can't get the basics down like this, it is only a matter of time before we get our asses collectively kicked by somebody who knows what good order and discipline actually is on a systemic level. Holy crap this was scary to read.

You better, and fast. You're an officer 24x7, and he's a SP4, 24x7.

Congratulations Captain, you have set a lower standard. However, it is easier to overcome this than a profound absence of Integrity.

You are an Officer all the time, just as he is a Specialist all the time, so He needs to address you as Sir or by your rank at all times. If you should take the conversation personal by using his first name then that's a different story.

On the spot correction needs to be swift and uncomfortable. Back when we used to wear BDU's and our rank was worn on the collar, I would pull on my collar and say, "Talk thru the microphone, I didn't hear you."
M. Downes, LTC (ret)

Yes, you should correct the soldier on the spot. You're to be addressed as either sir, or by your rank.

Find out his name and what unit he is in and report it to his NCO, and yes you should correct him