What’s the proper way to correct someone when not saluting an officer?

Excuse yourself from the major and drop that PFC for 20. Have her do a half-face and drop her for 20 more! Assign an NCO to see she gets into full battle gear for 20 laps around the entire hospital perimeter. She will salute you next time. Lol.

That one was always easy. Ask the soldier if his arm is injured. If he says no, then dress him down.

What happened to integrity? Who gives a shit if someone's feelings get hurt.

I had an officer tell me that my desire to ensure proper observation of customs and courtesies was admirable, I really didn't need to say to the Marine in question, "HEY, F***HEAD! GO BACK AND SALUTE THAT OFFICER, RETARD!"

No matter what you do someone is going to say you committed psychological violence against them. When we are supposed to salute then we do it in a crisp manner, period. Not doing so is wrong and this disregard and disrespect seems to only be getting worse. They act like it's a chore to render a salute much less a proper one, when it's an honor to even perform the courtesy in the first place...

I don’t think you were to aggressive

That is not aggressive if said in the right tone. In fact, if a strong effort was made by the officer in a humorous tone via a question, that’s the perfect way.

It depends on person who failed to salute. Someone that’s just out of basic/boot camp may never had contact with a commissioned officer and be a little flustered. More experienced (6+ months) enlisted personnel should have no excuse. That said, senior enlisted are usually more than happy take care of the matter. If they’re not there, I usually stop the individual and ask them whether they were taught to salute an officer. They’re usually embarrassed, snap off a quick salute, which I return. On a side note, I was the guest of honor at a recruit graduation several years ago. The incoming CO (an O-6) was taking my on a tour and several recruits failed to salute her. Her first question was what week they were in. If they were in the first three weeks, she would correct them and then take the name of the Recruit Division Commander. If they were in the middle three weeks, she was much more aggressive. And then again took the RDC’s name. My guess is the CMDCM got a call and request to follow up with the RDC. Then came a recruit that was close to graduation. Whoa, Nellie. He was blistered. I suspect the recruit’s RDC had to make a trip to see the new CO.

Chastise or correct in private.
Praise in public.
At least start out that way. If someone continues to repeat errors, making it public might help, it might not. But starting out the gate by publicly embarrassing someone who probably didn't intend to not respect your authority will most likely ensure they never do, even if they do salute you...

Boy am i glad I retired out when I did. The military is getting weak on discipline and on the spot corrections. If you can't get the soldiers to perform their most basic functions how the hell do you expect to get them to perform as a soldier/warrior when the time comes.