Hassan's scar from having his cleft lip surgically corrected is significant for a couple of reasons.
1. A "cleft" is a division, and Hassan's cleft lip is no different in that it represents the divisions that existed in Afghanistan while he was growing up and that still exist today. Because of his Hazara ethnicity, Hassan will never be equal to or truly unifiied with other Afghans (mainly the Pashtuns like Amir). When Baba pays to have Hassan's cleft lip corrected, Hassan still has a slight scar which illustrates that even if Afghanistan seems to have "corrected" itself on the surface, there will always be scars or reminders of its divisions.
2. Near the novel's end after his encounter with Assef, Amir recovers in the hospital with many injuries, but one that is significant is the scar that he now has on his upper lip from Assef hitting him. The scar represents not only the literal brotherhood between Amir and Hassan, but it like Hassan's scar will always be a reminder to Amir of what his redemption cost him and what that redemption was for--his betrayal of the physically and emotionally scarred Hassan.