The social issues which appear in Shirley Jackson's short story, "Charles", depend upon what one considers to be an issue personally. Some may look at Laurie's behavior as disrespectful and that can be considered a social issue. Others may not see this as a social issue based upon personal interpretation.
Social issues are, sometimes, hard to determine if one does not consider them to be an issue in the first place. That being said, here are the social issues one could determine to be found in the story.
1. Dis-respectfulness: Laurie is disrespectful to both his parents and his teacher. In today's society, many people deem dis-respectfulness as a social issue based upon the fact that children (and teens) fail to respect their parents and teachers as they have in prior generations.
2. Sexual gender issues: One could look at the fact that Laurie has a questionably obscure name as bringing attention to sexual gender issues. In generations past, names easily detailed if a person were a male or female. Cross-gender names were not typically given to children so as to define gender very early in life. The change in society today has allowed for the questioning of gender to more widely acceptable than during the times when Jackson wrote. Boys were named Charles or Mike or John. Boys played with army figures. Girls were named Ann or Sarah or Debbie. Girls played with dolls. Today, gender identity is not pushed as hard as it was in the past.
3. Parental involvement: In the story, Laurie repeatedly treas his parents disrespectfully. They fail to punish these behaviors. Again, social issues regarding this have been raised. Some have declared that parents simply are not as involved in their children's lives as they have in the past. Laurie's parents simply do not know him. They do not take the time to put one and one together regarding their child's behavior. Perhaps the failure of getting punished taught Laurie that it is okay to act the way that he does.