When correcting a subordinate, do you give a mild, but stern rebuke, or is yelling necessary, depending on the offense?

As a young lieutenant I was lucky enough to have the two greatest natural leaders I have ever met as my platoon sergeant and as the company 1stSgt. One was a Vietnam Vet; the other, Korea and Vietnam. They both had multiple medals for valor. (They became natural leaders, because it is natural when you do multiple combat tours to either become a good leader or find another line of work.)

They taught me that if you lose your mind and are frothing at the mouth emotionally amped up, when nobody is going to get hurt and nothing is going to get broke, you just sent a message. The message is that you can't keep calm in a non-crisis. The smart troops are going to wonder how bad you will unravel in a combat crap sandwich. Most high volume corrections are theater, and may not be the best way to go. I always assume a Marine did not intend to screw up, unless he proves otherwise.

Thereafter, I raised my voice to get someone's attention over a lot of background noise, to prevent imminent physical harm/injury, or to prevent property damage. I learned how to present a firm, serious explanation of what was expected, why it was expected, and the consequences of non-compliance. I also didn't jump someone's shit because of an unintended mistake. I just offered a calm, well-meant, appropriate reminder to keep aware.

In my experience (both military and civilian), a stern rebuke is mostly all I need at most to correct someone. I typically reserve raising my voice for occasions where I need to get someone's attention in a hurry to prevent serious injury, death, or severe equipment damage - basically when there's an urgent need to impress upon them the severity of the situation.

Given that I'm normally soft-spoken and a man of few words, raising my voice usually gets peoples' attention in a hurry.

Depends upon the individual offender. Never lose your presence, but some just need a reminder, others a longer instruction. Remember, you are trying to correct and prevent reoccurance. In more serious situations, shoot them quietly.