Injuries Sustained by Kylo Ren and Their Future Importance in the Story

I believe his disfiguration will follow his descent away from humanity & into the Dark Side, similar to every other major Sith except for Dooku.

 

So, we have (1) Wookie cross-bow bolt on the catwalk to Kylo's left side; (2) AT LEAST a glancing wound on the upper right arm by Finn; (3) a possible leg wound by Rey; (4) a thrust wound from Rey to his left shoulder; and (5) a cut wound starting at his right shoulder and continuing all the way up to the right side of his face. I speculate (6) that his hand didn't feel great when Rey cut his Emo lightsaber into pieces, but the shot of him on his back shows both hands intact. Depending upon how much source material is pulled from "Legends", we could also speculate that when he tracked down Vader's helmet, he also took Vader's gauntlets for himself, which as you saw in Empire, could block Han Solo's blaster bolts. This might have protected the hands from Rey's last cut.