These injuries may be territorial but regardless poor water quality can rile these P's up as well as high temps (80°+)
Try lowering temps to 74-76° and cut the light duration or intensity by removing a bulb or re positioning it higher or using black water extract.
And those "burn marks" look to me like the fish was cornered for awhile rubbing against dw, rock or piece of decor thus removing scales and inflicting a wound. My shoal has done this once before and it looked very similar.
Lower temps, don't over fed, keep up on wc, test water daily and lower light intensity and light duration. You could even throw in some guppies as dither fish to put more attention on them instead of the prized piranhas!
Either way you have plenty of solutions and imo lowering temps and less light has helped loads. Also stronger currents can break up aggression too, a korillia circulator may do the trick too:
http://www.petmountain.com/show_product/11442-522698
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Cheap way to decrease nitrates and keep your fish healthy:
http://monsterfishkeepers.com/forums/showthread.php?t=504763