I read some rather decent reasons for the 1/4 to 1/2 turn on this post. I'm an instructor, and recently got reprimanded by a DM in Cozumel for going back and checking my own air and making the 1/2 turn, after she completely forgot to turn my air on the previous dive. She said she would handle it, and that they always turned it back 1/2 turn. To make a long story short, I'm responsible for my own safety when diving, therefore, I will always check my own air and gear, no matter what anyone else says.
I had a dive buddy once who had just gotten certified that turned my air off, and then back on 1/2 turn while I was in a hurry working on something else, and didn't notice the hand that was on my valve knob. While at 63 ft. with about 700 psi, I noticed my SPG needle was fluctuating up and down with each breath. My training taught me that it was probably due to my valve not being opened far enough, so I didn't worry much about it, but terminated the dive anyway. I was impressed at how well my balanced reg set performed for an entire dive (until 700 psi) with such a small portion of the valve being opened!
Besides many of the reasons for turning the valve knob back 1/4 to 1/2 turn already mentioned, three of the main reasons I was taught years ago are:
1. If there is play in the valve, someone checking your valve should be able to tell very quickly that your air is turned on, without having to turn it back and forth several turns.
2. If there is play in the valve and you strike it on something hard while diving, or on a boat (i.e., overhead obstacle, bumping in to someone else's tank or side of the boat, etc.), then you may avoid damaging your valve, jamming it in the open position, or rendering it useless and dangerous. If it becomes severely damaged, then who knows if it might drain your tank dry in a hurry.
3. While under pressure, valves do strange and unpredictable things, like jamming open. The small turn back may not be necessary, but "an ounce of prevention," well, you know the story.
In the Open Water manual from the agency I teach for, it states to turn the valve all the way open, so that's how I teach my students in the classroom to conform to standards. However, I do mention the other options when gearing up for real-world diving so students can decide for themselves what they feel comfortable with. After all, it is their safety on the line in the long run.
After weighing the pros and cons, I have decided to stick with my old training habit of turning the valve knob back 1/4 to 1/2 turn...just in case.