His follow through, he's throwing across his body with the right shoulder whipping him toward the first base line in his release rather than more straight through to the plate, that's basically putting more torque on the shoulder and elbow. It also makes for nastier sliders or curves, but the greater torque on the shoulder and elbow takes a bigger toll on the ligaments, and the ligaments give out faster (usually) than straight follow through pitchers.
Every baseball player (especially pitchers) is damaging his arm to an extent no matter how good his mechanics are because the human body is designed to throw underhand, not overhand, but across the body type throwers usually pay the price sooner.
This eventually means major ligament surgery and a loss of velocity (and thus a less nasty breaking pitch) after recovery and some pitchers adjust to it and some don't. It seems to have sunk Kerry Wood, and Dwight Gooden had a similiar motion, but he had about 7 great years, then his arm gave out and he was just average after that. Pedro Martinez did it, he had some surgeries, lost some velocity and the nasty slider but made up for it by becoming more a location and change of speed pitcher. But for Peavy, there are no guarantees, he could be done, he could have 8 good years in him before he pays for those mechanics, but my guess is less since he's already having issues. The issues could linger, or he could have a major surgery and a long recovery time, and then he'd have to learn how to pitch with less velociy.
The problem is, this can sometimes happen in two stages, sometimes the shoulder gives out, it gets fixed, you adjust, then the elbow gives out, and you lose even more velocity.
To spot these guys, the two tells are: the pitcher falls off the mound towards the baseline, or the curve or slider is unnaturally nasty.
Some guy's have rubber arms and can get away with this longer than others, but this is usually a reliever's mechanics, guys like K-Rod. Relievers can have more years throwing like that because they're throwing fewer innings and spacing those innings out one or two innings at a time. Pitchers throwing 200 innings a year like that 7 or 9 innings at a time will give out much sooner.