For accuracy, wrinkles tend not to be evenly distributed around the bullet, putting its center of gravity off-center in the bore. That causes it to be flung away from the mean trajectory path at the exit from the muzzle, widening groups by drifting away from the center. Whether you have enough range and enough velocity in the drift away from the center to matter, depends on range, as suggested previously. But I have seen off-center bullet CG cause ten-shot .45 Auto target load groups sandbagged at 25 yards open from around an inch and three-eighths to about two inches. In that case, it was not wrinkles, but soft, short 185-grain swaged SWC's entering the throat slightly cocked that was causing the off-bore axis CG, and straightening their seating in the cases and going to headspacing on the bullet tightened things up. But that gives you some sense of the effect.
Symmetrical bullet bases are the most important single thing. If those get off-axis or deformed, the uneven play of muzzle blast gasses off the base of the bullet pushing it laterally away from the bore axis and it can introduce a surprising amount of initial yaw. The last thing is the reason asymmetrical muzzle crowns open groups up. There is an element of randomness to the exact effect of the gases, and in one case I saw it lead to keyholing, and random scatter.
Mind you, over a short enough range, even keyholing isn't a problem. Back when silenced .22's were considered the mark of the professional hitman, guns for that purpose would have the rifling reamed out to prevent ballistic matches from being made to recovered bullets (though you would think being caught with such a weapon would give the police a strong clue as to their suspect's occupation). Since the shots were fired at very close range, it made no practical difference. Hatcher even mentions the stopping power advantage of keyholing bullets. So everything depends on what your purposes are.
