OK. Yeah, this IS scheduled for a re-write
. I'll try and get to it this weekend.
The #3 "rotational slop" check means you put the gun in "full lockup" as described (hammer down, trigger back, just like you'd do when firing it) and you check to see if it spins just a bit. NOT enough to jump from the cylinder bore - if it does that, something is WAY wrong. No, you're checking for minuscule amounts of rotational play. On a Colt double action, early Charter Arms or other "tight lockup design", there'll be no play at all. On S&Ws, Rugers, Taurii and most others, there'll be some but it shouldn't be excessive - if the outside edge of the cylinder moves more than a millimeter or so, that's too much. This latter class is supposed to have a bit of rotational slop though, unless it's been custom gunsmithed.
Right, so assuming the cylinder is being locked in pretty tight, a later step involves making sure the barrel lines up with the cylinder bores via the flashlight trick or other methods. THAT is what tells you if the cylinder is being locked into a good place, or a bad place. This is more critical in the "tight designs" like the DA Colts that try and hold the cylinder dead firm. If it holds it firm in an out-of-alignment position, the gun tries to tear itself apart in short order...the bullets slam on the edge of the barrel's rear end because the alignment isn't right. In the S&W/Ruger/etc. "loose" types, as long as the alignment is "close" the bullet can spin the cylinder a tiny bit to create a proper alignment on firing - it's not quite as accurate, but it's more reliable and means fewer trips to see a gunsmith over the life of the gun.
Does that help?