Time for some fist a cuff action, on some topics that always gets the blood pumping, and the insults flying.
Damage to rifling - practically impossible with a carbon rod and all bronze brush, or just a flick of the wrist away from needing a new barrel?
Personally, I lean towards the former. With a carbon rod and all bronze jags / brushers, isn't that so much softer than rifling that it's like trying to scratch glass with your fingernails? Now with those foolish 3 piece steel rods we used in the Army - yes you could damage the rifling.
Direction of cleaning - old wives tale, or subject of vital importance?
Again, I lean towards the former, if using a good rod and bronze tools. Since I don't think you can damage the steel rifling with such softer gear, I don't think it matters which end you clean from. I also move the brush in and out of the bore - no bothering with taking it off after a pass, like I've seen some claim.
Pull patch back in, or might as well put dirt in it?
Some folks make a big deal about only running the patch in once. For me, if I'm using a slotted jag for whatever reason (like the barrel is long I can't push the jag far enough to get the patch out with the length of rod I have (that's what she said!!)), I just pull it back out again, and horror of horrors, that dirty patch is going back through the barrel. But most of the crud stays on the patch, and if any does go back on the bore, it'll come up with the next few patches.
So for me:
If it's a short barrel like on a pistol, just for GP, I'll clean chamber to bore, and pull the brush back through the barrel. Then with patches, use a solid jag, and push them through, flip the patch over, and push them through again on the cleaner side.
But for rifles, such as AR's, I'll clean them muzzle to chamber as it's easier to have the end of the barrel sticking off the bench and run the patch in that way. Use a slotted jag as with the small 22 cal bore, and a flash hider, I can't center a patch to be able to push a solid jag onto it. Brush and patch both ways.
What says ya?