The 360 rig is sometimes pinned with mouth damage due to its mechanics, in the same way the long shank bent hook rig was in the 80-90s - indeed this rig was banned in many places. The long shank aspect used to "double hook" (hook through the lips multiple times, otherwise called stitching) and then tear in the carps mouth, the bent hook, if not bent correctly, would open and close at the point of bending kind of like an old fashioned can opener causing damage to the carp.
The fox series 5 - the first commercially available long shanked curved hook brought in to try and emulate the success of the bent hook rig. It was found that smaller, more frantic carp could "double hook" themselves which then tore, ripping the lips. The readon shrink tube became so popular was it allowed you to fish a "bent hook" which didnt cause the damage with the hook opening and closing like a can openerin the carps mouth this is why we bend and curve shrink tube, to emulate the bent hook rig.The link has been made between the longshanked aspect and the 360 rig, it has been said (by "them") that it can cause the double hooking which leads to mouth damage. The evidence is not exactly solid, in the case of the bent hook rig, the damage and its cause was obvious, and lots of lakes banned it. The 360 rig is used by many top anglers, mr dave lane being one of them, it is seen as a "big fish rig" mostly down to the fact it utilises a longshanked hook which can hook multiple times in a smaller carps mouth. It is also designed to be fished heavily weighted as opposed to critically balanced. The idea is that the pop up spins 360 degrees and hook in the bottom lip. The use of a longshank hook has always been linked to mouth damage to smaller carp. Whether its true or not? Well thats open to speculation, the old bent hook was brutal, but the 360 rig is well popular and well used, if it was as damaging as the old bent hook rig was, then we would know by now, its been out for years, i dont use it as its too much metal in/around the hook - plus the use of a longshank puts me off a bit, as i remember the mouth damage from the 1st longshank curved hooks and bent hook rigs. I havent seen the series 5 on sale for years, although fox do sell the armapoint LSC which look near as damn it identical.