The main event that might classify this short story as a mystery is the lack of specific details and closure at the very end of it. After Jimmy saves little Agnes from the safe--in the process revealing himself to be a handy safe-breaker and potential criminal--a couple interesting things happen that O. Henry doesn't explain in detail. The first is that Ben Price, who has spent a significant amount of his career trying to capture the infamous and elusive Jimmy Valentine, and who has travelled miles to arrest him, just lets Jimmy go. He knows who Jimmy is, and has finally cornered him. But instead, he nods Jimmy on his way, plays along with Jimmy's game, and lets him go free. Why? This is a mystery--there is no indication that he would have done that. We are left wondering and scratching our heads.
The second mystery of the story centers around why Jimmy leaves after savng Agnes. It could be one of two reasons--either he knew he had revealed himself as a criminal and knew his fiance and family wouldn't accept him anymore, OR, that breaking into the safe had revived his old love for the thrill of robbing banks, and he knew that he couldn't "settle down" to a life of domesticity. We aren't told which one prompts him to leave--so, it is a mystery. Another mystery is what happens after Ben Price lets him off the hook--does Jimmy go back in? Or, does he keep walking, leaving behind his new life forever? We don't know. It's a mystery.
For those reasons, there are elements of mystery to O. Henry's story "A Retrieved Reformation." I hope that helped; good luck!